Theorem necon3abii 2281

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 2246	. 2 |- ( A =/= B <-> -. A = B )
2		necon3abii.1	. 2 |- ( A = B <-> ph )
3	1, 2	xchbinx 639	1 |- ( A =/= B <-> -. ph )

Syntax hints:   -. wn 3   <-> wb 103   = wceq 1284   =/= wne 2245

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577

This theorem depends on definitions:  df-bi 115  df-ne 2246

This theorem is referenced by:  necon3bbii  2282  necon3bii  2283  nesym  2290  n0rf  3260  gcd0id  10370