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Theorem neeq12d 2367
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 2365 . 2 (𝜑 → (𝐴𝐶𝐵𝐶))
3 neeq12d.2 . . 3 (𝜑𝐶 = 𝐷)
43neeq2d 2366 . 2 (𝜑 → (𝐵𝐶𝐵𝐷))
52, 4bitrd 188 1 (𝜑 → (𝐴𝐶𝐵𝐷))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 105   = wceq 1353  wne 2347
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-5 1447  ax-gen 1449  ax-4 1510  ax-17 1526  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-cleq 2170  df-ne 2348
This theorem is referenced by:  3netr3d  2379  3netr4d  2380  exmidapne  7258  ennnfonelemim  12424  ctinfom  12428  isnzr  13323  apdiff  14766
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