Theorem frege63b 39042

Description: Lemma for frege91 39088. Proposition 63 of [Frege1879] p. 52. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.)

Assertion

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

Proof of Theorem frege63b

Step	Hyp	Ref	Expression
1		frege62b 39041	. 2 ⊢ ([𝑥 / 𝑦]𝜑 → (∀𝑦(𝜑 → 𝜒) → [𝑥 / 𝑦]𝜒))
2		frege24 38949	. 2 ⊢ (([𝑥 / 𝑦]𝜑 → (∀𝑦(𝜑 → 𝜒) → [𝑥 / 𝑦]𝜒)) → ([𝑥 / 𝑦]𝜑 → (𝜓 → (∀𝑦(𝜑 → 𝜒) → [𝑥 / 𝑦]𝜒))))
3	1, 2	ax-mp 5	1 ⊢ ([𝑥 / 𝑦]𝜑 → (𝜓 → (∀𝑦(𝜑 → 𝜒) → [𝑥 / 𝑦]𝜒)))

Syntax hints:   → wi 4  ∀wal 1656  [wsb 2069

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-10 2194  ax-12 2222  ax-13 2391  ax-frege1 38924  ax-frege2 38925  ax-frege8 38943  ax-frege58b 39035

This theorem depends on definitions:  df-bi 199  df-an 387  df-or 881  df-ex 1881  df-nf 1885  df-sb 2070

This theorem is referenced by: (None)