Theorem pm5.35 823

Description: Theorem *5.35 of [WhiteheadRussell] p. 125. Closed form of 2thd 264. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm5.35	⊢ (((𝜑 → 𝜓) ∧ (𝜑 → 𝜒)) → (𝜑 → (𝜓 ↔ 𝜒)))

Proof of Theorem pm5.35

Step	Hyp	Ref	Expression
1		pm5.1 821	. 2 ⊢ (((𝜑 → 𝜓) ∧ (𝜑 → 𝜒)) → ((𝜑 → 𝜓) ↔ (𝜑 → 𝜒)))
2	1	pm5.74rd 273	1 ⊢ (((𝜑 → 𝜓) ∧ (𝜑 → 𝜒)) → (𝜑 → (𝜓 ↔ 𝜒)))

Syntax hints:   → wi 4   ↔ wb 205   ∧ wa 396

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 397

This theorem is referenced by: (None)