Theorem necon2bi 1609

Description: Contrapositive inference for inequality.

Hypothesis

Ref	Expression
necon2bi.1	|- (ph -> A =/= B)

Assertion

Ref	Expression
necon2bi	|- (A = B -> -. ph)

Proof of Theorem necon2bi

Step	Hyp	Ref	Expression
1		necon2bi.1	. . 3 |- (ph -> A =/= B)
2		df-ne 1584	. . 3 |- (A =/= B <-> -. A = B)
3	1, 2	sylib 198	. 2 |- (ph -> -. A = B)
4	3	con2i 97	1 |- (A = B -> -. ph)

Syntax hints:  -. wn 2   -> wi 3   = wceq 954   =/= wne 1582

This theorem is referenced by:  minel 2320  dtrucor2 2769  nlim0 3022  kmlem6 4750  0npi 4990  0npr 5076

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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