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Theorem 3netr3g 3015
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 3003 . 2 (𝐴𝐵𝐶𝐷)
51, 4sylib 209 1 (𝜑𝐶𝐷)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1652  wne 2937
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2070  ax-7 2105  ax-9 2164  ax-ext 2743
This theorem depends on definitions:  df-bi 198  df-an 385  df-ex 1875  df-cleq 2758  df-ne 2938
This theorem is referenced by: (None)
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