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Theorem neneqad 2325
Description: If it is not the case that two classes are equal, they are unequal. Converse of neneqd 2267. One-way deduction form of df-ne 2247. (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 590 . 2 (𝐴 = 𝐵 → ¬ 𝜑)
32necon2ai 2300 1 (𝜑𝐴𝐵)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   = wceq 1285  wne 2246
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 577  ax-in2 578
This theorem depends on definitions:  df-bi 115  df-ne 2247
This theorem is referenced by:  ne0i  3264  nsuceq0g  4181  fidifsnen  6405  nqnq0pi  6690  xrlttri3  8948  expival  9575
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