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Theorem xchbinxr 607
Description: Replacement of a subexpression by an equivalent one. (Contributed by Wolf Lammen, 27-Sep-2014.)
Hypotheses
Ref Expression
xchbinxr.1 (φ ↔ ¬ ψ)
xchbinxr.2 (χψ)
Assertion
Ref Expression
xchbinxr (φ ↔ ¬ χ)

Proof of Theorem xchbinxr
StepHypRef Expression
1 xchbinxr.1 . 2 (φ ↔ ¬ ψ)
2 xchbinxr.2 . . 3 (χψ)
32bicomi 123 . 2 (ψχ)
41, 3xchbinx 606 1 (φ ↔ ¬ χ)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  xordc1  1281  sbnv  1765  ralnex  2310  difab  3200  disjsn  3423  iindif2m  3715  reldm0  4496
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