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Theorem neeq1d 2218
Description: Deduction for inequality. (Contributed by NM, 25-Oct-1999.)
Hypothesis
Ref Expression
neeq1d.1 (φA = B)
Assertion
Ref Expression
neeq1d (φ → (A𝐶B𝐶))

Proof of Theorem neeq1d
StepHypRef Expression
1 neeq1d.1 . 2 (φA = B)
2 neeq1 2213 . 2 (A = B → (A𝐶B𝐶))
31, 2syl 14 1 (φ → (A𝐶B𝐶))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98   = 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  ax-5 1333  ax-gen 1335  ax-4 1397  ax-17 1416  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-ne 2203
This theorem is referenced by:  neeq12d  2220  eqnetrd  2223  prnzg  3483
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