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Metamath Proof Explorer

Theorem orbi12i

Description: Infer the disjunction of two equivalences. (Contributed by NM, 3-Jan-1993)

Ref Expression
Hypotheses orbi12i.1 ⊢ φ ↔ ψ
orbi12i.2 ⊢ χ ↔ θ
Assertion orbi12i ⊢ φ ∨ χ ↔ ψ ∨ θ

Proof

Step Hyp Ref Expression
1 orbi12i.1 ⊢ φ ↔ ψ
2 orbi12i.2 ⊢ χ ↔ θ
3 2 orbi2i ⊢ φ ∨ χ ↔ φ ∨ θ
4 1 orbi1i ⊢ φ ∨ θ ↔ ψ ∨ θ
5 3 4 bitri ⊢ φ ∨ χ ↔ ψ ∨ θ