Metamath Proof Explorer

Theorem 3anbi13d

Description: Deduction conjoining and adding a conjunct to equivalences. (Contributed by NM, 8-Sep-2006)

Ref Expression
Hypotheses 3anbi12d.1 φ ψ χ
3anbi12d.2 φ θ τ
Assertion 3anbi13d φ ψ η θ χ η τ


Step Hyp Ref Expression
1 3anbi12d.1 φ ψ χ
2 3anbi12d.2 φ θ τ
3 biidd φ η η
4 1 3 2 3anbi123d φ ψ η θ χ η τ