Theorem pm5.35 837

Description: Theorem *5.35 of [WhiteheadRussell] p. 125. Closed form of 2thd 268. (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		pm5.1 835	. 2 ⊢ (((𝜑 → 𝜓) ∧ (𝜑 → 𝜒)) → ((𝜑 → 𝜓) ↔ (𝜑 → 𝜒)))
2	1	pm5.74rd 277	1 ⊢ (((𝜑 → 𝜓) ∧ (𝜑 → 𝜒)) → (𝜑 → (𝜓 ↔ 𝜒)))

This proof depends on syntax axioms:   → wi 4   ↔ wb 209   ∧ wa 400

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 401

This theorem is used by: (None)