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Theorem dcn 746

Description: A decidable proposition is decidable when negated. (Contributed by Jim Kingdon, 25-Mar-2018.)

**Assertion**
Ref	Expression
dcn	DECID DECID

**Proof of Theorem dcn**
Step	Hyp	Ref	Expression
1		notnot 559	. . . 4
2	1	orim2i 678	. . 3 $\/$ $\/$
3	2	orcoms 649	. 2 $\/$ $\/$
4		df-dc 743	. 2 DECID $\/$
5		df-dc 743	. 2 DECID $\/$
6	3, 4, 5	3imtr4i 190	1 DECID DECID

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $\/$ 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: pm5.18dc 777 pm4.67dc 781 pm2.54dc 790 imordc 796 pm4.54dc 805 stabtestimpdc 824 annimdc 845 pm4.55dc 846 pm3.12dc 865 pm3.13dc 866 dn1dc 867 xor3dc 1278 dfbi3dc 1288 dcned 2212