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Theorem neeq1d 2529
 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 2524 . 2 (A = B → (ACBC))
31, 2syl 15 1 (φ → (ACBC))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   = wceq 1642   ≠ wne 2516 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-ex 1542  df-cleq 2346  df-ne 2518 This theorem is referenced by:  neeq12d  2531  eqnetrd  2534  prnzg  3836  preaddccan2lem1  4454  preaddccan2  4455  evenodddisj  4516  vfinncvntnn  4548  ereldm  5971  map0  6025  ce0addcnnul  6179  ce0nn  6180  ce0nnulb  6182
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