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Theorem xchbinx 640
Description: Replacement of a subexpression by an equivalent one. (Contributed by Wolf Lammen, 27-Sep-2014.)
Hypotheses
Ref Expression
xchbinx.1  |-  ( ph  <->  -. 
ps )
xchbinx.2  |-  ( ps  <->  ch )
Assertion
Ref Expression
xchbinx  |-  ( ph  <->  -. 
ch )

Proof of Theorem xchbinx
StepHypRef Expression
1 xchbinx.1 . 2  |-  ( ph  <->  -. 
ps )
2 xchbinx.2 . . 3  |-  ( ps  <->  ch )
32notbii 627 . 2  |-  ( -. 
ps 
<->  -.  ch )
41, 3bitri 182 1  |-  ( ph  <->  -. 
ch )
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:  xchbinxr  641  necon3abii  2282  elirr  4292  en2lp  4305  dm0rn0  4580
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