Theorem necon2i 2261

Description: Contrapositive inference for inequality. (Contributed by NM, 18-Mar-2007.)

Hypothesis

Ref	Expression
necon2i.1	|- ( A = B -> C =/= D )

Assertion

Ref	Expression
necon2i	|- ( C = D -> A =/= B )

Proof of Theorem necon2i

Step	Hyp	Ref	Expression
1		necon2i.1	. . 3 |- ( A = B -> C =/= D )
2	1	neneqd 2226	. 2 |- ( A = B -> -. C = D )
3	2	necon2ai 2259	1 |- ( C = D -> A =/= B )

Syntax hints:   -> wi 4   = wceq 1243   =/= wne 2204

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545

This theorem depends on definitions:  df-bi 110  df-ne 2206

This theorem is referenced by: (None)