Theorem pm4.76 528

Description: Theorem *4.76 of [WhiteheadRussell] p. 121. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.76	⊢ (((𝜑 → 𝜓) ∧ (𝜑 → 𝜒)) ↔ (𝜑 → (𝜓 ∧ 𝜒)))

Proof of Theorem pm4.76

Step	Hyp	Ref	Expression
1		jcab 527	. 2 ⊢ ((𝜑 → (𝜓 ∧ 𝜒)) ↔ ((𝜑 → 𝜓) ∧ (𝜑 → 𝜒)))
2	1	bicomi 227	1 ⊢ (((𝜑 → 𝜓) ∧ (𝜑 → 𝜒)) ↔ (𝜑 → (𝜓 ∧ 𝜒)))

This proof depends on syntax axioms:   → wi 4   ↔ wb 209   ∧ wa 401

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 402

This theorem is used by:  fun11  6614  axgroth4  10834  bj-alnnf  37421  dford4  43816  undmrnresiss  44390