Theorem frege63b 43217

Description: Lemma for frege91 43263. Proposition 63 of [Frege1879] p. 52. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
frege63b	⊢ ([𝑦 / 𝑥]𝜑 → (𝜓 → (∀𝑥(𝜑 → 𝜒) → [𝑦 / 𝑥]𝜒)))

Proof of Theorem frege63b

Step	Hyp	Ref	Expression
1		frege62b 43216	. 2 ⊢ ([𝑦 / 𝑥]𝜑 → (∀𝑥(𝜑 → 𝜒) → [𝑦 / 𝑥]𝜒))
2		frege24 43124	. 2 ⊢ (([𝑦 / 𝑥]𝜑 → (∀𝑥(𝜑 → 𝜒) → [𝑦 / 𝑥]𝜒)) → ([𝑦 / 𝑥]𝜑 → (𝜓 → (∀𝑥(𝜑 → 𝜒) → [𝑦 / 𝑥]𝜒))))
3	1, 2	ax-mp 5	1 ⊢ ([𝑦 / 𝑥]𝜑 → (𝜓 → (∀𝑥(𝜑 → 𝜒) → [𝑦 / 𝑥]𝜒)))

Syntax hints:   → wi 4  ∀wal 1531  [wsb 2059

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-10 2129  ax-12 2163  ax-frege1 43099  ax-frege2 43100  ax-frege8 43118  ax-frege58b 43210

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-ex 1774  df-nf 1778  df-sb 2060

This theorem is referenced by: (None)