Metamath Proof Explorer

Theorem 3orbi123

Description: pm4.39 with a 3-conjunct antecedent. This proof is 3orbi123VD automatically translated and minimized. (Contributed by Alan Sare, 31-Dec-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion 3orbi123 ⊢ φ ↔ ψ ∧ χ ↔ θ ∧ τ ↔ η → φ ∨ χ ∨ τ ↔ ψ ∨ θ ∨ η

Proof

Step Hyp Ref Expression
1 simp1 ⊢ φ ↔ ψ ∧ χ ↔ θ ∧ τ ↔ η → φ ↔ ψ
2 simp2 ⊢ φ ↔ ψ ∧ χ ↔ θ ∧ τ ↔ η → χ ↔ θ
3 simp3 ⊢ φ ↔ ψ ∧ χ ↔ θ ∧ τ ↔ η → τ ↔ η
4 1 2 3 3orbi123d ⊢ φ ↔ ψ ∧ χ ↔ θ ∧ τ ↔ η → φ ∨ χ ∨ τ ↔ ψ ∨ θ ∨ η