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Theorem xchnxbi 320
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 308 . 2 𝜑 ↔ ¬ 𝜒)
3 xchnxbi.1 . 2 𝜑𝜓)
42, 3bitr3i 264 1 𝜒𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 194
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 195
This theorem is referenced by:  xchnxbir  321  ioran  509  pm5.24  933  2mo  2535  necon1bbii  2827  nabbi  2880  psslinpr  9706  isprm2lem  15175
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