ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  cdeqnot GIF version

Theorem cdeqnot 2752
Description: Distribute conditional equality over negation. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
cdeqnot.1 CondEq(𝑥 = 𝑦 → (𝜑𝜓))
Assertion
Ref Expression
cdeqnot CondEq(𝑥 = 𝑦 → (¬ 𝜑 ↔ ¬ 𝜓))

Proof of Theorem cdeqnot
StepHypRef Expression
1 cdeqnot.1 . . . 4 CondEq(𝑥 = 𝑦 → (𝜑𝜓))
21cdeqri 2750 . . 3 (𝑥 = 𝑦 → (𝜑𝜓))
32notbid 592 . 2 (𝑥 = 𝑦 → (¬ 𝜑 ↔ ¬ 𝜓))
43cdeqi 2749 1 CondEq(𝑥 = 𝑦 → (¬ 𝜑 ↔ ¬ 𝜓))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 98  CondEqwcdeq 2747
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545
This theorem depends on definitions:  df-bi 110  df-cdeq 2748
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator