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Theorem xchbinx 682
Description: Replacement of a subexpression by an equivalent one. (Contributed by Wolf Lammen, 27-Sep-2014.)
Hypotheses
Ref Expression
xchbinx.1 (𝜑 ↔ ¬ 𝜓)
xchbinx.2 (𝜓𝜒)
Assertion
Ref Expression
xchbinx (𝜑 ↔ ¬ 𝜒)

Proof of Theorem xchbinx
StepHypRef Expression
1 xchbinx.1 . 2 (𝜑 ↔ ¬ 𝜓)
2 xchbinx.2 . . 3 (𝜓𝜒)
32notbii 668 . 2 𝜓 ↔ ¬ 𝜒)
41, 3bitri 184 1 (𝜑 ↔ ¬ 𝜒)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 105
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  xchbinxr  683  necon3abii  2383  elirr  4540  en2lp  4553  dm0rn0  4844
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