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Theorem neeq12i 2222
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 2221 . 2 (𝐴𝐶𝐴𝐷)
3 neeq1i.1 . . 3 𝐴 = 𝐵
43neeq1i 2220 . 2 (𝐴𝐷𝐵𝐷)
52, 4bitri 173 1 (𝐴𝐶𝐵𝐷)
Colors of variables: wff set class
Syntax hints:  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:  3netr3g  2239  3netr4g  2240
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