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Theorem neeqtrd 2538
Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012.)
Hypotheses
Ref Expression
neeqtrd.1 (φAB)
neeqtrd.2 (φB = C)
Assertion
Ref Expression
neeqtrd (φAC)

Proof of Theorem neeqtrd
StepHypRef Expression
1 neeqtrd.1 . 2 (φAB)
2 neeqtrd.2 . . 3 (φB = C)
32neeq2d 2530 . 2 (φ → (ABAC))
41, 3mpbid 201 1 (φAC)
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:  neeqtrrd  2540
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