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Theorem 3netr3d 2542
Description: Substitution of equality into both sides of an inequality. (Contributed by NM, 24-Jul-2012.)
Hypotheses
Ref Expression
3netr3d.1
3netr3d.2
3netr3d.3
Assertion
Ref Expression
3netr3d

Proof of Theorem 3netr3d
StepHypRef Expression
1 3netr3d.1 . 2
2 3netr3d.2 . . 3
3 3netr3d.3 . . 3
42, 3neeq12d 2531 . 2
51, 4mpbid 201 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wceq 1642   wne 2516
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-ex 1542  df-cleq 2346  df-ne 2518
This theorem is referenced by: (None)
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