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Theorem frege66b 38522
Description: Swap antecedents of frege65b 38521. 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 38521 . 2 (∀𝑥(𝜒𝜑) → (∀𝑥(𝜑𝜓) → ([𝑦 / 𝑥]𝜒 → [𝑦 / 𝑥]𝜓)))
2 ax-frege8 38420 . 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 1521  [wsb 1937
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-10 2059  ax-12 2087  ax-13 2282  ax-frege1 38401  ax-frege2 38402  ax-frege8 38420  ax-frege58b 38512
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1745  df-nf 1750  df-sb 1938
This theorem is referenced by: (None)
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