nndc - Mathbox for BJ

	Mathbox for BJ		< Previous Next > Nearby theorems
Mirrors > Home > ILE Home > Th. List > Mathboxes > nndc		Unicode version

Theorem nndc 9900

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 9899	. 2 $\/$
2		df-dc 743	. . 3 DECID $\/$
3	2	notbii 594	. 2 DECID $\/$
4	1, 3	mtbir 596	1 DECID

Colors of variables: wff set class

Syntax hints:

wn 3 $\/$ wo 629 DECID wdc 742

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630

This theorem depends on definitions: df-bi 110 df-dc 743

This theorem is referenced by: dcdc 9901

W3C validator