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Theorem neneqad 2278
Description: If it is not the case that two classes are equal, they are unequal. Converse of neneqd 2221. One-way deduction form of df-ne 2203. (Contributed by David Moews, 28-Feb-2017.)
Hypothesis
Ref Expression
neneqad.1 (φ → ¬ A = B)
Assertion
Ref Expression
neneqad (φAB)

Proof of Theorem neneqad
StepHypRef Expression
1 neneqad.1 . . 3 (φ → ¬ A = B)
21con2i 557 . 2 (A = B → ¬ φ)
32necon2ai 2253 1 (φAB)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1242  wne 2201
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-ne 2203
This theorem is referenced by:  ne0i  3224  nsuceq0g  4121  nqnq0pi  6420  xrlttri3  8448  expival  8871
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