Theorem necon3abii 1588

Description: Deduction from equality to inequality.

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 1579	. 2 |- (A =/= B <-> -. A = B)
2		necon3abii.1	. . 3 |- (A = B <-> ph)
3	2	negbii 187	. 2 |- (-. A = B <-> -. ph)
4	1, 3	bitr 173	1 |- (A =/= B <-> -. ph)

Syntax hints:  -. wn 2   <-> wb 146   = wceq 953   =/= wne 1577

This theorem is referenced by:  necon3bbii 1589  necon3bii 1590  rankxplim3 4686  rankxpsuc 4687  h1de2bOLD 9393  h1de2ctlem 9394

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 1579

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