Metamath Proof Explorer

Theorem pm4.72

Description: Implication in terms of biconditional and disjunction. Theorem *4.72 of WhiteheadRussell p. 121. (Contributed by NM, 30-Aug-1993) (Proof shortened by Wolf Lammen, 30-Jan-2013)

Ref Expression
Assertion pm4.72 φ ψ ψ φ ψ


Step Hyp Ref Expression
1 olc ψ φ ψ
2 pm2.621 φ ψ φ ψ ψ
3 1 2 impbid2 φ ψ ψ φ ψ
4 orc φ φ ψ
5 biimpr ψ φ ψ φ ψ ψ
6 4 5 syl5 ψ φ ψ φ ψ
7 3 6 impbii φ ψ ψ φ ψ