Theorem necon3bbii 1594

Description: Deduction from equality to inequality.

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 172	. . 3 |- (A = B <-> ph)
3	2	necon3abii 1593	. 2 |- (A =/= B <-> -. ph)
4	3	bicomi 172	1 |- (-. ph <-> A =/= B)

Syntax hints:  -. wn 2   <-> wb 146   = wceq 954   =/= wne 1582

This theorem is referenced by:  tfi 3121  oelim2 4212  bcthlem9 7957  shne0 9309  pjnel 9608  cnfilca 10487

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-ne 1584

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