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Theorem necon3bii 2293
Description: Inference from equality to inequality. (Contributed by NM, 23-Feb-2005.)
Hypothesis
Ref Expression
necon3bii.1 (𝐴 = 𝐵𝐶 = 𝐷)
Assertion
Ref Expression
necon3bii (𝐴𝐵𝐶𝐷)

Proof of Theorem necon3bii
StepHypRef Expression
1 necon3bii.1 . . 3 (𝐴 = 𝐵𝐶 = 𝐷)
21necon3abii 2291 . 2 (𝐴𝐵 ↔ ¬ 𝐶 = 𝐷)
3 df-ne 2256 . 2 (𝐶𝐷 ↔ ¬ 𝐶 = 𝐷)
42, 3bitr4i 185 1 (𝐴𝐵𝐶𝐷)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 103   = wceq 1289  wne 2255
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 579  ax-in2 580
This theorem depends on definitions:  df-bi 115  df-ne 2256
This theorem is referenced by:  necom  2339  negne0bi  7734
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