nndc - Mathbox for BJ

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Theorem nndc 10722

Description: Double negation of decidability of a formula. Intuitionistic logic refutes undecidability (but, of course, does not prove decidability) of any formula. (Contributed by BJ, 9-Oct-2019.)

**Assertion**
Ref	Expression
nndc	DECID

**Proof of Theorem nndc**
Step	Hyp	Ref	Expression
1		nnexmid 10721	. 2 $\/$
2		df-dc 777	. . 3 DECID $\/$
3	2	notbii 627	. 2 DECID $\/$
4	1, 3	mtbir 629	1 DECID

Colors of variables: wff set class

Syntax hints:

wn 3 $\/$ wo 662 DECID wdc 776

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 577 ax-in2 578 ax-io 663

This theorem depends on definitions: df-bi 115 df-dc 777

This theorem is referenced by: dcdc 10723

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