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Theorem neeq12d 2225
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 2223 . 2 (𝜑 → (𝐴𝐶𝐵𝐶))
3 neeq12d.2 . . 3 (𝜑𝐶 = 𝐷)
43neeq2d 2224 . 2 (𝜑 → (𝐵𝐶𝐵𝐷))
52, 4bitrd 177 1 (𝜑 → (𝐴𝐶𝐵𝐷))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98   = wceq 1243  wne 2204
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 1336  ax-gen 1338  ax-4 1400  ax-17 1419  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-cleq 2033  df-ne 2206
This theorem is referenced by:  3netr3d  2237  3netr4d  2238
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