Theorem pm4.39 992

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 488	. 2 ⊢ (((𝜑 ↔ 𝜒) ∧ (𝜓 ↔ 𝜃)) → (𝜑 ↔ 𝜒))
2		simpr 490	. 2 ⊢ (((𝜑 ↔ 𝜒) ∧ (𝜓 ↔ 𝜃)) → (𝜓 ↔ 𝜃))
3	1, 2	orbi12d 932	1 ⊢ (((𝜑 ↔ 𝜒) ∧ (𝜓 ↔ 𝜃)) → ((𝜑 ∨ 𝜓) ↔ (𝜒 ∨ 𝜃)))

This proof depends on syntax axioms:   → wi 4   ↔ wb 209   ∧ wa 401   ∨ wo 861

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  df-or 862

This theorem is used by:  3orbi123VD  45659