Theorem pm4.76 519

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 518	. 2 ⊢ ((𝜑 → (𝜓 ∧ 𝜒)) ↔ ((𝜑 → 𝜓) ∧ (𝜑 → 𝜒)))
2	1	bicomi 223	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:  fun11  6508  axgroth4  10588  dford4  40851  undmrnresiss  41212