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Theorem neeq12i 2266
Description: Inference for inequality. (Contributed by NM, 24-Jul-2012.)
Hypotheses
Ref Expression
neeq1i.1 𝐴 = 𝐵
neeq12i.2 𝐶 = 𝐷
Assertion
Ref Expression
neeq12i (𝐴𝐶𝐵𝐷)

Proof of Theorem neeq12i
StepHypRef Expression
1 neeq12i.2 . . 3 𝐶 = 𝐷
21neeq2i 2265 . 2 (𝐴𝐶𝐴𝐷)
3 neeq1i.1 . . 3 𝐴 = 𝐵
43neeq1i 2264 . 2 (𝐴𝐷𝐵𝐷)
52, 4bitri 182 1 (𝐴𝐶𝐵𝐷)
Colors of variables: wff set class
Syntax hints:  wb 103   = wceq 1285  wne 2249
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 2065
This theorem depends on definitions:  df-bi 115  df-cleq 2076  df-ne 2250
This theorem is referenced by:  3netr3g  2283  3netr4g  2284
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