Theorem pm5.74ri 237

Description: Distribution of implication over biconditional (reverse inference rule). (Contributed by NM, 1-Aug-1994.)

Hypothesis

Ref	Expression
pm5.74ri.1	|- ((ph -> ps) <-> (ph -> ch))

Assertion

Ref	Expression
pm5.74ri	|- (ph -> (ps <-> ch))

Proof of Theorem pm5.74ri

Step	Hyp	Ref	Expression
1		pm5.74ri.1	. 2 |- ((ph -> ps) <-> (ph -> ch))
2		pm5.74 235	. 2 |- ((ph -> (ps <-> ch)) <-> ((ph -> ps) <-> (ph -> ch)))
3	1, 2	mpbir 200	1 |- (ph -> (ps <-> ch))

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:  bitrd  244  bibi2d  309  tbt  333  sbco2d  2087  2mos  2283