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Theorem xchnxbir 639
Description: Replacement of a subexpression by an equivalent one. (Contributed by Wolf Lammen, 27-Sep-2014.)
Hypotheses
Ref Expression
xchnxbir.1  |-  ( -. 
ph 
<->  ps )
xchnxbir.2  |-  ( ch  <->  ph )
Assertion
Ref Expression
xchnxbir  |-  ( -. 
ch 
<->  ps )

Proof of Theorem xchnxbir
StepHypRef Expression
1 xchnxbir.1 . 2  |-  ( -. 
ph 
<->  ps )
2 xchnxbir.2 . . 3  |-  ( ch  <->  ph )
32bicomi 130 . 2  |-  ( ph  <->  ch )
41, 3xchnxbi 638 1  |-  ( -. 
ch 
<->  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> 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  ax-in1 577  ax-in2 578
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  3ioran  935  truxortru  1351  truxorfal  1352  falxortru  1353  falxorfal  1354  intirr  4741  sizeunlem  9828
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