Theorem necon1i 2827

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

Hypothesis

Ref	Expression
necon1i.1	|- ( A =/= B -> C = D )

Assertion

Ref	Expression
necon1i	|- ( C =/= D -> A = B )

Proof of Theorem necon1i

Step	Hyp	Ref	Expression
1		df-ne 2795	. . 3 |- ( A =/= B <-> -. A = B )
2		necon1i.1	. . 3 |- ( A =/= B -> C = D )
3	1, 2	sylbir 225	. 2 |- ( -. A = B -> C = D )
4	3	necon1ai 2821	1 |- ( C =/= D -> A = B )

Syntax hints:   -. wn 3   -> wi 4   = wceq 1483   =/= wne 2794

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 197  df-ne 2795

This theorem is referenced by: (None)