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Theorem necon3bii 2548
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 2546 . 2 (AB ↔ ¬ C = D)
3 df-ne 2518 . 2 (CD ↔ ¬ C = D)
42, 3bitr4i 243 1 (ABCD)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 176   = wceq 1642  wne 2516
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 177  df-ne 2518
This theorem is referenced by:  necom  2597  nulnnn  4556  rnsnn0  5065  ce2  6192  nchoicelem14  6302
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