Theorem frege61b 41514

Description: Lemma for frege65b 41518. Proposition 61 of [Frege1879] p. 52. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege61b	⊢ (([𝑥 / 𝑦]𝜑 → 𝜓) → (∀𝑦𝜑 → 𝜓))

Proof of Theorem frege61b

Step	Hyp	Ref	Expression
1		ax-frege58b 41509	. 2 ⊢ (∀𝑦𝜑 → [𝑥 / 𝑦]𝜑)
2		frege9 41420	. 2 ⊢ ((∀𝑦𝜑 → [𝑥 / 𝑦]𝜑) → (([𝑥 / 𝑦]𝜑 → 𝜓) → (∀𝑦𝜑 → 𝜓)))
3	1, 2	ax-mp 5	1 ⊢ (([𝑥 / 𝑦]𝜑 → 𝜓) → (∀𝑦𝜑 → 𝜓))

Syntax hints:   → wi 4  ∀wal 1537  [wsb 2067

This theorem was proved from axioms:  ax-mp 5  ax-frege1 41398  ax-frege2 41399  ax-frege8 41417  ax-frege58b 41509

This theorem is referenced by:  frege65b  41518