Theorem necon1bbii 1614

Description: Contrapositive inference for inequality.

Hypothesis

Ref	Expression
necon1bbii.1	|- (A =/= B <-> ph)

Assertion

Ref	Expression
necon1bbii	|- (-. ph <-> A = B)

Proof of Theorem necon1bbii

Step	Hyp	Ref	Expression
1		df-ne 1584	. . 3 |- (A =/= B <-> -. A = B)
2		necon1bbii.1	. . 3 |- (A =/= B <-> ph)
3	1, 2	bitr3 175	. 2 |- (-. A = B <-> ph)
4	3	con1bii 220	1 |- (-. ph <-> A = B)

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

This theorem is referenced by:  necon2bbii 1618  rab0 2289  intnex 2725  class2set 2729  relimasn 3417  fvprc 3712  fvopabn 3777  oarec 4186  dffsum 6944  climunii 7043  dfisum 7135  hlimunii 9047

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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