Theorem necon2bi 1612

Description: Contrapositive inference for inequality.

Hypothesis

Ref	Expression
necon2bi.1	|- (ph -> A =/= B)

Assertion

Ref	Expression
necon2bi	|- (A = B -> -. ph)

Proof of Theorem necon2bi

Step	Hyp	Ref	Expression
1		necon2bi.1	. . 3 |- (ph -> A =/= B)
2		df-ne 1587	. . 3 |- (A =/= B <-> -. A = B)
3	1, 2	sylib 198	. 2 |- (ph -> -. A = B)
4	3	con2i 97	1 |- (A = B -> -. ph)

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

This theorem is referenced by:  minel 2324  dtrucor2 2774  nlim0 3027  kmlem6 4770  0npi 5010  0npr 5096

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