Theorem necon3abii 2403

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 2368	. 2 |- ( A =/= B <-> -. A = B )
2		necon3abii.1	. 2 |- ( A = B <-> ph )
3	1, 2	xchbinx 683	1 |- ( A =/= B <-> -. ph )

Syntax hints:   -. wn 3   <-> wb 105   = wceq 1364   =/= wne 2367

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616

This theorem depends on definitions:  df-bi 117  df-ne 2368

This theorem is referenced by:  necon3bbii  2404  necon3bii  2405  nesym  2412  n0rf  3463  gcd0id  12146