exmidne - Metamath Proof Explorer

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Theorem exmidne 2804

Description: Excluded middle with equality and inequality. (Contributed by NM, 3-Feb-2012.) (Proof shortened by Wolf Lammen, 17-Nov-2019.)

**Assertion**
Ref	Expression
exmidne	$\/$

**Proof of Theorem exmidne**
Step	Hyp	Ref	Expression
1		neqne 2802	. 2
2	1	orri 391	1 $\/$

Colors of variables: wff setvar class

Syntax hints: $\/$ wo 383

wceq 1483

wne 2794

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

This theorem depends on definitions: df-bi 197 df-or 385 df-ne 2795

This theorem is referenced by: elnn1uz2 11765 hashv01gt1 13133 subfacp1lem6 31167 tendoeq2 36062 ax6e2ndeqVD 39145 ax6e2ndeqALT 39167