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Theorem necon3d 2554

Description: Contrapositive law deduction for inequality. (Contributed by NM, 10-Jun-2006.)

**Hypothesis**
Ref	Expression
necon3d.1

**Assertion**
Ref	Expression
necon3d

**Proof of Theorem necon3d**
Step	Hyp	Ref	Expression
1		necon3d.1	. . 3
2	1	necon3ad 2552	. 2
3		df-ne 2518	. 2
4	2, 3	syl6ibr 218	1

Colors of variables: wff setvar class

Syntax hints:

wn 3

wi 4

wceq 1642

wne 2516

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8

This theorem depends on definitions: df-bi 177 df-ne 2518

This theorem is referenced by: necon3i 2555 pm13.18 2588 ssn0 3583 pssdifn0 3611 uniintsn 3963 evenodddisj 4516 sfinltfin 4535 leltctr 6212 nnltp1c 6262