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Theorem dcor 937

Description: A disjunction of two decidable propositions is decidable. (Contributed by Jim Kingdon, 21-Apr-2018.)

**Assertion**
Ref	Expression
dcor	DECID DECID DECID $\/$

**Proof of Theorem dcor**
Step	Hyp	Ref	Expression
1		df-dc 836	. 2 DECID $\/$
2		orc 713	. . . . . 6 $\/$
3	2	orcd 734	. . . . 5 $\/$ $\/$ $\/$
4		df-dc 836	. . . . 5 DECID $\/$ $\/$ $\/$ $\/$
5	3, 4	sylibr 134	. . . 4 DECID $\/$
6	5	a1d 22	. . 3 DECID DECID $\/$
7		df-dc 836	. . . . 5 DECID $\/$
8		olc 712	. . . . . . . . 9 $\/$
9	8	adantl 277	. . . . . . . 8 $/\$ $\/$
10	9	orcd 734	. . . . . . 7 $/\$ $\/$ $\/$ $\/$
11	10, 4	sylibr 134	. . . . . 6 $/\$ DECID $\/$
12		ioran 753	. . . . . . . . 9 $\/$ $/\$
13	12	biimpri 133	. . . . . . . 8 $/\$ $\/$
14	13	olcd 735	. . . . . . 7 $/\$ $\/$ $\/$ $\/$
15	14, 4	sylibr 134	. . . . . 6 $/\$ DECID $\/$
16	11, 15	jaodan 798	. . . . 5 $/\$ $\/$ DECID $\/$
17	7, 16	sylan2b 287	. . . 4 $/\$ DECID DECID $\/$
18	17	ex 115	. . 3 DECID DECID $\/$
19	6, 18	jaoi 717	. 2 $\/$ DECID DECID $\/$
20	1, 19	sylbi 121	1 DECID DECID DECID $\/$

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $/\$ wa 104 $\/$ wo 709 DECID wdc 835

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710

This theorem depends on definitions: df-bi 117 df-dc 836

This theorem is referenced by: pm4.55dc 940 orandc 941 pm3.12dc 960 pm3.13dc 961 dn1dc 962 eueq3dc 2938 distrlem4prl 7668 distrlem4pru 7669 exfzdc 10333 lcmmndc 12255 isprm3 12311 perfectlem2 15320 lgsval 15329 lgsfvalg 15330 lgsfcl2 15331 lgsval2lem 15335 lgsdir2 15358 lgsne0 15363 lgsdirnn0 15372 lgsdinn0 15373 2lgs 15429 2lgsoddprm 15438 cndcap 15790