Theorem necon3abii 2546

Description: Deduction from equality to inequality. (Contributed by NM, 9-Nov-2007.)

Hypothesis

Ref	Expression
necon3abii.1	|- (A = B <-> ph)

Assertion

Ref	Expression
necon3abii	|- (A =/= B <-> -. ph)

Proof of Theorem necon3abii

Step	Hyp	Ref	Expression
1		df-ne 2518	. 2 |- (A =/= B <-> -. A = B)
2		necon3abii.1	. 2 |- (A = B <-> ph)
3	1, 2	xchbinx 301	1 |- (A =/= B <-> -. ph)

Syntax hints:  -. wn 3   <-> wb 176   = wceq 1642   =/= wne 2516

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 2518

This theorem is referenced by:  necon3bbii  2547  necon3bii  2548  necompl  3544  n0f  3558  foconst  5280