Theorem nndc 836

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

Assertion

Ref	Expression
nndc	|- -. -. DECID ph

Proof of Theorem nndc

Step	Hyp	Ref	Expression
1		nnexmid 835	. 2 |- -. -. ( ph \/ -. ph )
2		df-dc 820	. . 3 |- (DECID ph <-> ( ph \/ -. ph ) )
3	2	notbii 657	. 2 |- ( -. DECID ph <-> -. ( ph \/ -. ph ) )
4	1, 3	mtbir 660	1 |- -. -. DECID ph

Syntax hints:   -. wn 3   \/ wo 697  DECID wdc 819

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  df-dc 820

This theorem is referenced by:  bj-nnst  12964  bj-dcdc  12965  bj-stdc  12966