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Theorem xchbinxr 672
Description: Replacement of a subexpression by an equivalent one. (Contributed by Wolf Lammen, 27-Sep-2014.)
Hypotheses
Ref Expression
xchbinxr.1  |-  ( ph  <->  -. 
ps )
xchbinxr.2  |-  ( ch  <->  ps )
Assertion
Ref Expression
xchbinxr  |-  ( ph  <->  -. 
ch )

Proof of Theorem xchbinxr
StepHypRef Expression
1 xchbinxr.1 . 2  |-  ( ph  <->  -. 
ps )
2 xchbinxr.2 . . 3  |-  ( ch  <->  ps )
32bicomi 131 . 2  |-  ( ps  <->  ch )
41, 3xchbinx 671 1  |-  ( ph  <->  -. 
ch )
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:  xordc1  1371  sbnv  1860  ralnex  2424  difab  3340  disjsn  3580  iindif2m  3875  reldm0  4752
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