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Theorem xchnxbir 670
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 131 . 2  |-  ( ph  <->  ch )
41, 3xchnxbi 669 1  |-  ( -. 
ch 
<->  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  3ioran  977  truxortru  1397  truxorfal  1398  falxortru  1399  falxorfal  1400  intirr  4920  hashunlem  10543
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