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Theorem necon2bi 2562
Description: Contrapositive inference for inequality. (Contributed by NM, 1-Apr-2007.)
Hypothesis
Ref Expression
necon2bi.1 (φAB)
Assertion
Ref Expression
necon2bi (A = B → ¬ φ)

Proof of Theorem necon2bi
StepHypRef Expression
1 necon2bi.1 . . 3 (φAB)
21neneqd 2532 . 2 (φ → ¬ A = B)
32con2i 112 1 (A = B → ¬ φ)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4   = 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:  necon4i  2576  minel  3606  rzal  3651  difsnb  3850  nulnnc  6118
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