nnexmid - Intuitionistic Logic Explorer

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Theorem nnexmid 835

Description: Double negation of excluded middle. Intuitionistic logic refutes the negation of excluded middle (but does not prove excluded middle) for any formula. Can also be proved quickly from bj-nnor 12935 as in bj-nndcALT 12952. (Contributed by BJ, 9-Oct-2019.)

**Assertion**
Ref	Expression
nnexmid	$\/$

**Proof of Theorem nnexmid**
Step	Hyp	Ref	Expression
1		pm3.24 682	. 2 $/\$
2		ioran 741	. 2 $\/$ $/\$
3	1, 2	mtbir 660	1 $\/$

Colors of variables: wff set class

Syntax hints:

wn 3 $/\$ wa 103 $\/$ wo 697

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 603 ax-in2 604 ax-io 698

This theorem depends on definitions: df-bi 116

This theorem is referenced by: nndc 836 exmid1stab 13184

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