Theorem frege63b 37222

Description: Lemma for frege91 37268. 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 37221	. 2 ⊢ ([𝑥 / 𝑦]𝜑 → (∀𝑦(𝜑 → 𝜒) → [𝑥 / 𝑦]𝜒))
2		frege24 37129	. 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 1473  [wsb 1867

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-12 2034  ax-13 2234  ax-frege1 37104  ax-frege2 37105  ax-frege8 37123  ax-frege58b 37215

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868

This theorem is referenced by: (None)