Theorem necon1bd 1624

Description: Contrapositive deduction for inequality.

Hypothesis

Ref	Expression
necon1bd.1	|- (ph -> (A =/= B -> ps))

Assertion

Ref	Expression
necon1bd	|- (ph -> (-. ps -> A = B))

Proof of Theorem necon1bd

Step	Hyp	Ref	Expression
1		necon1bd.1	. . 3 |- (ph -> (A =/= B -> ps))
2		df-ne 1579	. . 3 |- (A =/= B <-> -. A = B)
3	1, 2	syl5ibr 207	. 2 |- (ph -> (-. A = B -> ps))
4	3	con1d 93	1 |- (ph -> (-. ps -> A = B))

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

This theorem is referenced by:  ordsseleq 2966  tfinds 3151  fvclss 3840  sqr0 6602  inelr 6665  sncld 7726  elspansn5t 9414  atoml 10217

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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