Theorem pm5.74ri 647

Description: Distribution of implication over biconditional (reverse inference rule).

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		pm5.74 643	. 2 |- ((ph -> (ps <-> ch)) <-> ((ph -> ps) <-> (ph -> ch)))
3	1, 2	mpbir 207	1 |- (ph -> (ps <-> ch))

Syntax hints:   -> wi 3   <-> wb 163

This theorem is referenced by:  pm5.501 655  iba 704  ibar 705  tbt 788  sbco2d 1630  cbvaldOLD 1703  2mos 1852  sbc2ie 2523  sbc2iedv 2524  nn0ltp1le 7336  axgroth6 10137  isprm2 13775

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 164  df-an 242

Copyright terms: Public domain