Metamath Proof Explorer


Theorem impbida

Description: Deduce an equivalence from two implications. Variant of impbid . (Contributed by NM, 17-Feb-2007)

Ref Expression
Hypotheses impbida.1 φ ψ χ
impbida.2 φ χ ψ
Assertion impbida φ ψ χ

Proof

Step Hyp Ref Expression
1 impbida.1 φ ψ χ
2 impbida.2 φ χ ψ
3 1 ex φ ψ χ
4 2 ex φ χ ψ
5 3 4 impbid φ ψ χ