Theorem pm4.39 834

Description: Theorem *4.39 of [WhiteheadRussell] p. 118. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.39	⊢ (((𝜑 ↔ 𝜒) ∧ (𝜓 ↔ 𝜃)) → ((𝜑 ∨ 𝜓) ↔ (𝜒 ∨ 𝜃)))

Proof of Theorem pm4.39

Step	Hyp	Ref	Expression
1		simpl 109	. 2 ⊢ (((𝜑 ↔ 𝜒) ∧ (𝜓 ↔ 𝜃)) → (𝜑 ↔ 𝜒))
2		simpr 110	. 2 ⊢ (((𝜑 ↔ 𝜒) ∧ (𝜓 ↔ 𝜃)) → (𝜓 ↔ 𝜃))
3	1, 2	orbi12d 805	1 ⊢ (((𝜑 ↔ 𝜒) ∧ (𝜓 ↔ 𝜃)) → ((𝜑 ∨ 𝜓) ↔ (𝜒 ∨ 𝜃)))

This proof depends on syntax axioms:   → wi 4   ∧ wa 104   ↔ wb 105   ∨ wo 720

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721

This proof depends on definitions:  df-bi 117

This theorem is used by: (None)