Theorem necon3abii 2372

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 2337	. 2 |- ( A =/= B <-> -. A = B )
2		necon3abii.1	. 2 |- ( A = B <-> ph )
3	1, 2	xchbinx 672	1 |- ( A =/= B <-> -. ph )

Syntax hints:   -. wn 3   <-> wb 104   = wceq 1343   =/= wne 2336

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605

This theorem depends on definitions:  df-bi 116  df-ne 2337

This theorem is referenced by:  necon3bbii  2373  necon3bii  2374  nesym  2381  n0rf  3421  gcd0id  11912