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Theorem 3netr4d 2543
Description: Substitution of equality into both sides of an inequality. (Contributed by NM, 24-Jul-2012.)
Hypotheses
Ref Expression
3netr4d.1 (φAB)
3netr4d.2 (φC = A)
3netr4d.3 (φD = B)
Assertion
Ref Expression
3netr4d (φCD)

Proof of Theorem 3netr4d
StepHypRef Expression
1 3netr4d.1 . 2 (φAB)
2 3netr4d.2 . . 3 (φC = A)
3 3netr4d.3 . . 3 (φD = B)
42, 3neeq12d 2531 . 2 (φ → (CDAB))
51, 4mpbird 223 1 (φCD)
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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