Metamath Proof Explorer


Theorem ibib

Description: Implication in terms of implication and biconditional. (Contributed by NM, 31-Mar-1994) (Proof shortened by Wolf Lammen, 24-Jan-2013)

Ref Expression
Assertion ibib φ ψ φ φ ψ

Proof

Step Hyp Ref Expression
1 pm5.501 φ ψ φ ψ
2 1 pm5.74i φ ψ φ φ ψ