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Theorem necon1bbii 2568
Description: Contrapositive inference for inequality. (Contributed by NM, 17-Mar-2007.)
Hypothesis
Ref Expression
necon1bbii.1 (ABφ)
Assertion
Ref Expression
necon1bbii φA = B)

Proof of Theorem necon1bbii
StepHypRef Expression
1 df-ne 2518 . . 3 (AB ↔ ¬ A = B)
2 necon1bbii.1 . . 3 (ABφ)
31, 2bitr3i 242 . 2 A = Bφ)
43con1bii 321 1 φA = B)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 176   = wceq 1642  wne 2516
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-ne 2518
This theorem is referenced by:  necon2bbii  2572  rabeq0  3572
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