Theorem necon4i 1625

Description: Contrapositive inference for inequality.

Hypothesis

Ref	Expression
necon4i.1	|- (A =/= B -> C =/= D)

Assertion

Ref	Expression
necon4i	|- (C = D -> A = B)

Proof of Theorem necon4i

Step	Hyp	Ref	Expression
1		necon4i.1	. . 3 |- (A =/= B -> C =/= D)
2		df-ne 1587	. . 3 |- (C =/= D <-> -. C = D)
3	1, 2	sylib 198	. 2 |- (A =/= B -> -. C = D)
4	3	necon4ai 1624	1 |- (C = D -> A = B)

Syntax hints:  -. wn 2   -> wi 3   = wceq 956   =/= wne 1585

This theorem is referenced by:  map0 4344  scott0 4717

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 1587

Copyright terms: Public domain