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Theorem bianabs 578
Description: Absorb a hypothesis into the second member of a biconditional. (Contributed by FL, 15-Feb-2007.)
Hypothesis
Ref Expression
bianabs.1  |-  ( ph  ->  ( ps  <->  ( ph  /\ 
ch ) ) )
Assertion
Ref Expression
bianabs  |-  ( ph  ->  ( ps  <->  ch )
)

Proof of Theorem bianabs
StepHypRef Expression
1 bianabs.1 . 2  |-  ( ph  ->  ( ps  <->  ( ph  /\ 
ch ) ) )
2 ibar 295 . 2  |-  ( ph  ->  ( ch  <->  ( ph  /\ 
ch ) ) )
31, 2bitr4d 189 1  |-  ( ph  ->  ( ps  <->  ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    <-> 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:  ceqsrexv  2745  opelopab2a  4083  ov  5746  ovg  5765  ltresr  7355
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