Metamath Proof Explorer


Theorem ibibr

Description: Implication in terms of implication and biconditional. (Contributed by NM, 29-Apr-2005) (Proof shortened by Wolf Lammen, 21-Dec-2013)

Ref Expression
Assertion ibibr φ ψ φ ψ φ

Proof

Step Hyp Ref Expression
1 pm5.501 φ ψ φ ψ
2 bicom φ ψ ψ φ
3 1 2 bitrdi φ ψ ψ φ
4 3 pm5.74i φ ψ φ ψ φ