Theorem necon3bi 1610

Description: Contrapositive inference for inequality.

Hypothesis

Ref	Expression
necon3bi.1	|- (A = B -> ph)

Assertion

Ref	Expression
necon3bi	|- (-. ph -> A =/= B)

Proof of Theorem necon3bi

Step	Hyp	Ref	Expression
1		necon3bi.1	. . 3 |- (A = B -> ph)
2	1	con3i 98	. 2 |- (-. ph -> -. A = B)
3		df-ne 1590	. 2 |- (A =/= B <-> -. A = B)
4	2, 3	sylibr 200	1 |- (-. ph -> A =/= B)

Syntax hints:  -. wn 2   -> wi 3   = wceq 958   =/= wne 1588

This theorem is referenced by:  alephord 4886  acdc3lem 7487  acdc2lem1 7489  acdclem 7495

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-ne 1590

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