Theorem ibib 331

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

Assertion

Ref	Expression
ibib	|- ((ph -> ps) <-> (ph -> (ph <-> ps)))

Proof of Theorem ibib

Step	Hyp	Ref	Expression
1		pm5.501 330	. 2 |- (ph -> (ps <-> (ph <-> ps)))
2	1	pm5.74i 236	1 |- ((ph -> ps) <-> (ph -> (ph <-> ps)))

This proof depends on syntax axioms:   -> wi 4   <-> wb 176

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177

This theorem is used by: (None)