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Theorem xchnxbi 638
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 627 . 2 𝜑 ↔ ¬ 𝜒)
3 xchnxbi.1 . 2 𝜑𝜓)
42, 3bitr3i 184 1 𝜒𝜓)
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:  xchnxbir  639
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