Theorem necon3bbii 2242

Description: Deduction from equality to inequality. (Contributed by NM, 13-Apr-2007.)

Hypothesis

Ref	Expression
necon3bbii.1	|- ( ph <-> A = B )

Assertion

Ref	Expression
necon3bbii	|- ( -. ph <-> A =/= B )

Proof of Theorem necon3bbii

Step	Hyp	Ref	Expression
1		necon3bbii.1	. . . 4 |- ( ph <-> A = B )
2	1	bicomi 123	. . 3 |- ( A = B <-> ph )
3	2	necon3abii 2241	. 2 |- ( A =/= B <-> -. ph )
4	3	bicomi 123	1 |- ( -. ph <-> A =/= B )

Syntax hints:   -. wn 3   <-> wb 98   = wceq 1243   =/= wne 2204

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545

This theorem depends on definitions:  df-bi 110  df-ne 2206

This theorem is referenced by:  nssinpss  3169  difsnpssim  3507