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Theorem frege67b 37674
Description: Lemma for frege68b 37675. Proposition 67 of [Frege1879] p. 54. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
frege67b (((∀𝑥𝜑𝜓) → (𝜓 → ∀𝑥𝜑)) → ((∀𝑥𝜑𝜓) → (𝜓 → [𝑦 / 𝑥]𝜑)))

Proof of Theorem frege67b
StepHypRef Expression
1 ax-frege58b 37663 . 2 (∀𝑥𝜑 → [𝑦 / 𝑥]𝜑)
2 frege7 37570 . 2 ((∀𝑥𝜑 → [𝑦 / 𝑥]𝜑) → (((∀𝑥𝜑𝜓) → (𝜓 → ∀𝑥𝜑)) → ((∀𝑥𝜑𝜓) → (𝜓 → [𝑦 / 𝑥]𝜑))))
31, 2ax-mp 5 1 (((∀𝑥𝜑𝜓) → (𝜓 → ∀𝑥𝜑)) → ((∀𝑥𝜑𝜓) → (𝜓 → [𝑦 / 𝑥]𝜑)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wal 1478  [wsb 1882
This theorem was proved from axioms:  ax-mp 5  ax-frege1 37552  ax-frege2 37553  ax-frege58b 37663
This theorem is referenced by:  frege68b  37675
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