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Theorem pm2.21ddne 2282
Description: A contradiction implies anything. Equality/inequality deduction form. (Contributed by David Moews, 28-Feb-2017.)
Hypotheses
Ref Expression
pm2.21ddne.1 (φA = B)
pm2.21ddne.2 (φAB)
Assertion
Ref Expression
pm2.21ddne (φψ)

Proof of Theorem pm2.21ddne
StepHypRef Expression
1 pm2.21ddne.1 . 2 (φA = B)
2 pm2.21ddne.2 . . 3 (φAB)
32neneqd 2221 . 2 (φ → ¬ A = B)
41, 3pm2.21dd 550 1 (φψ)
Colors of variables: wff set class
Syntax hints:  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-in2 545
This theorem depends on definitions:  df-bi 110  df-ne 2203
This theorem is referenced by: (None)
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