ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm5.74i Unicode version

Theorem pm5.74i 178
Description: Distribution of implication over biconditional (inference form). (Contributed by NM, 1-Aug-1994.)
Hypothesis
Ref Expression
pm5.74i.1  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
pm5.74i  |-  ( (
ph  ->  ps )  <->  ( ph  ->  ch ) )

Proof of Theorem pm5.74i
StepHypRef Expression
1 pm5.74i.1 . 2  |-  ( ph  ->  ( ps  <->  ch )
)
2 pm5.74 177 . 2  |-  ( (
ph  ->  ( ps  <->  ch )
)  <->  ( ( ph  ->  ps )  <->  ( ph  ->  ch ) ) )
31, 2mpbi 143 1  |-  ( (
ph  ->  ps )  <->  ( ph  ->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  bitrd  186  imbi2i  224  bibi2d  230  ibib  243  ibibr  244  anclb  312  pm5.42  313  ancrb  315  equsalh  1661  equsal  1662  sb6a  1912  ralbiia  2392  dfdif3  3110  raaan  3388  exmid01  4032  isprm4  11379
  Copyright terms: Public domain W3C validator