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Theorem frege66c 37705
 Description: Swap antecedents of frege65c 37704. Proposition 66 of [Frege1879] p. 54. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
frege59c.a 𝐴𝐵
Assertion
Ref Expression
frege66c (∀𝑥(𝜑𝜓) → (∀𝑥(𝜒𝜑) → ([𝐴 / 𝑥]𝜒[𝐴 / 𝑥]𝜓)))

Proof of Theorem frege66c
StepHypRef Expression
1 frege59c.a . . 3 𝐴𝐵
21frege65c 37704 . 2 (∀𝑥(𝜒𝜑) → (∀𝑥(𝜑𝜓) → ([𝐴 / 𝑥]𝜒[𝐴 / 𝑥]𝜓)))
3 ax-frege8 37585 . 2 ((∀𝑥(𝜒𝜑) → (∀𝑥(𝜑𝜓) → ([𝐴 / 𝑥]𝜒[𝐴 / 𝑥]𝜓))) → (∀𝑥(𝜑𝜓) → (∀𝑥(𝜒𝜑) → ([𝐴 / 𝑥]𝜒[𝐴 / 𝑥]𝜓))))
42, 3ax-mp 5 1 (∀𝑥(𝜑𝜓) → (∀𝑥(𝜒𝜑) → ([𝐴 / 𝑥]𝜒[𝐴 / 𝑥]𝜓)))
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1478   ∈ wcel 1987  [wsbc 3417 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-12 2044  ax-13 2245  ax-ext 2601  ax-frege1 37566  ax-frege2 37567  ax-frege8 37585  ax-frege58b 37677 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-v 3188  df-sbc 3418 This theorem is referenced by: (None)
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