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lines changed Original file line number Diff line number Diff line change @@ -571203,6 +571203,18 @@ Real and complex numbers (cont.)
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currybi $p |- ( ( ph <-> ( ph <-> ps ) ) -> ps ) $=
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( wb biid biass biimpri mpbii ) AABCCZAACZBADIBCHAABEFG $.
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+ $( Suppose ` ph ` , ` ps ` are distinct atomic propositional formulas, and
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+ let ` _G ` be the smallest class of formulas for which ` T. e. _G ` and
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+ ` ( ch -> ph ) ` , ` ( ch -> ps ) e. _G ` for ` ch e. _G ` . The present
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+ theorem is then an element of ` _G ` , and the implications occurring in
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+ the theorem are in one-to-one correspondence with the formulas in ` _G `
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+ up to logical equivalence. In particular, the theorem itself is
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+ equivalent to ` T. e. _G ` . (Contributed by Adrian Ducourtial,
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+ 2-Oct-2025.) $)
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+ antnest $p |- ( ( ( ( ( ( T. -> ph ) -> ps ) -> ps ) -> ph ) -> ps ) -> ps )
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+ $=
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+ ( wtru wi wn simplim conax1 mtod syl syl11 mptru pm2.65i notnotri ) CADZBDZ
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+ BDZADZBDZBDZSEZATADOECATNBFTOBRBGZTQEZPTQBUARBFHZPAFIHJKTUBAEUCPAGILM $.
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$(
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