Theorem necon1bbid 1611

Description: Contrapositive inference for inequality.

Hypothesis

Ref	Expression
necon1bbid.1	|- (ph -> (A =/= B <-> ps))

Assertion

Ref	Expression
necon1bbid	|- (ph -> (-. ps <-> A = B))

Proof of Theorem necon1bbid

Step	Hyp	Ref	Expression
1		necon1bbid.1	. . 3 |- (ph -> (A =/= B <-> ps))
2		df-ne 1579	. . 3 |- (A =/= B <-> -. A = B)
3	1, 2	syl5bbr 532	. 2 |- (ph -> (-. A = B <-> ps))
4	3	con1bid 525	1 |- (ph -> (-. ps <-> A = B))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 146   = wceq 953   =/= wne 1577

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-an 225  df-ne 1579

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