Theorem necon2i 2564

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 2533	. 2 |- (A = B -> -. C = D)
3	2	necon2ai 2562	1 |- (C = D -> A =/= B)

Syntax hints:   -> wi 4   = wceq 1642   =/= wne 2517

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 2519

This theorem is referenced by:  map0  6026