Theorem frege63b 43926

Description: Lemma for frege91 43972. 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 43925	. 2 ⊢ ([𝑦 / 𝑥]𝜑 → (∀𝑥(𝜑 → 𝜒) → [𝑦 / 𝑥]𝜒))
2		frege24 43833	. 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 1537  [wsb 2063

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-10 2140  ax-12 2176  ax-frege1 43808  ax-frege2 43809  ax-frege8 43827  ax-frege58b 43919

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1779  df-nf 1783  df-sb 2064

This theorem is referenced by: (None)