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Theorem neeq12d 2266
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 2264 . 2 (𝜑 → (𝐴𝐶𝐵𝐶))
3 neeq12d.2 . . 3 (𝜑𝐶 = 𝐷)
43neeq2d 2265 . 2 (𝜑 → (𝐵𝐶𝐵𝐷))
52, 4bitrd 186 1 (𝜑 → (𝐴𝐶𝐵𝐷))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 103   = 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  ax-5 1377  ax-gen 1379  ax-4 1441  ax-17 1460  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-cleq 2075  df-ne 2247
This theorem is referenced by:  3netr3d  2278  3netr4d  2279
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