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Theorem xchnxbi 333
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 321 . 2 𝜑 ↔ ¬ 𝜒)
3 xchnxbi.1 . 2 𝜑𝜓)
42, 3bitr3i 278 1 𝜒𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 207
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 208
This theorem is referenced by:  xchnxbir  334  ioran  977  pm5.24  1042  2mo  2726  necon1bbii  3062  nabbi  3118  psslinpr  10441
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