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Theorem frege66b 37714
Description: Swap antecedents of frege65b 37713. Proposition 66 of [Frege1879] p. 54. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege66b (∀𝑥(𝜑𝜓) → (∀𝑥(𝜒𝜑) → ([𝑦 / 𝑥]𝜒 → [𝑦 / 𝑥]𝜓)))

Proof of Theorem frege66b
StepHypRef Expression
1 frege65b 37713 . 2 (∀𝑥(𝜒𝜑) → (∀𝑥(𝜑𝜓) → ([𝑦 / 𝑥]𝜒 → [𝑦 / 𝑥]𝜓)))
2 ax-frege8 37612 . 2 ((∀𝑥(𝜒𝜑) → (∀𝑥(𝜑𝜓) → ([𝑦 / 𝑥]𝜒 → [𝑦 / 𝑥]𝜓))) → (∀𝑥(𝜑𝜓) → (∀𝑥(𝜒𝜑) → ([𝑦 / 𝑥]𝜒 → [𝑦 / 𝑥]𝜓))))
31, 2ax-mp 5 1 (∀𝑥(𝜑𝜓) → (∀𝑥(𝜒𝜑) → ([𝑦 / 𝑥]𝜒 → [𝑦 / 𝑥]𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1478  [wsb 1877
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-10 2016  ax-12 2044  ax-13 2245  ax-frege1 37593  ax-frege2 37594  ax-frege8 37612  ax-frege58b 37704
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1702  df-nf 1707  df-sb 1878
This theorem is referenced by: (None)
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