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Theorem neeq12d 2220
 Description: Deduction for inequality. (Contributed by NM, 24-Jul-2012.)
Hypotheses
Ref Expression
neeq1d.1 (φA = B)
neeq12d.2 (φ𝐶 = 𝐷)
Assertion
Ref Expression
neeq12d (φ → (A𝐶B𝐷))

Proof of Theorem neeq12d
StepHypRef Expression
1 neeq1d.1 . . 3 (φA = B)
21neeq1d 2218 . 2 (φ → (A𝐶B𝐶))
3 neeq12d.2 . . 3 (φ𝐶 = 𝐷)
43neeq2d 2219 . 2 (φ → (B𝐶B𝐷))
52, 4bitrd 177 1 (φ → (A𝐶B𝐷))
 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:  3netr3d  2231  3netr4d  2232
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