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Theorem xchnxbi 654
Description: Replacement of a subexpression by an equivalent one. (Contributed by Wolf Lammen, 27-Sep-2014.)
Hypotheses
Ref Expression
xchnxbi.1 𝜑𝜓)
xchnxbi.2 (𝜑𝜒)
Assertion
Ref Expression
xchnxbi 𝜒𝜓)

Proof of Theorem xchnxbi
StepHypRef Expression
1 xchnxbi.2 . . 3 (𝜑𝜒)
21notbii 642 . 2 𝜑 ↔ ¬ 𝜒)
3 xchnxbi.1 . 2 𝜑𝜓)
42, 3bitr3i 185 1 𝜒𝜓)
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 588  ax-in2 589
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  xchnxbir  655
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