Metamath Proof Explorer

Theorem pm4.39

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

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

Proof

Step Hyp Ref Expression
1 simpl ⊢ φ ↔ χ ∧ ψ ↔ θ → φ ↔ χ
2 simpr ⊢ φ ↔ χ ∧ ψ ↔ θ → ψ ↔ θ
3 1 2 orbi12d ⊢ φ ↔ χ ∧ ψ ↔ θ → φ ∨ ψ ↔ χ ∨ θ