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Theorem 3netr3g 2285
Description: Substitution of equality into both sides of an inequality. (Contributed by NM, 24-Jul-2012.)
Hypotheses
Ref Expression
3netr3g.1 (𝜑𝐴𝐵)
3netr3g.2 𝐴 = 𝐶
3netr3g.3 𝐵 = 𝐷
Assertion
Ref Expression
3netr3g (𝜑𝐶𝐷)

Proof of Theorem 3netr3g
StepHypRef Expression
1 3netr3g.1 . 2 (𝜑𝐴𝐵)
2 3netr3g.2 . . 3 𝐴 = 𝐶
3 3netr3g.3 . . 3 𝐵 = 𝐷
42, 3neeq12i 2268 . 2 (𝐴𝐵𝐶𝐷)
51, 4sylib 120 1 (𝜑𝐶𝐷)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1287  wne 2251
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 1379  ax-gen 1381  ax-4 1443  ax-17 1462  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-cleq 2078  df-ne 2252
This theorem is referenced by: (None)
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