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Theorem dcor 948

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 847	. 2 DECID $\/$
2		orc 724	. . . . . 6 $\/$
3	2	orcd 745	. . . . 5 $\/$ $\/$ $\/$
4		df-dc 847	. . . . 5 DECID $\/$ $\/$ $\/$ $\/$
5	3, 4	sylibr 134	. . . 4 DECID $\/$
6	5	a1d 22	. . 3 DECID DECID $\/$
7		df-dc 847	. . . . 5 DECID $\/$
8		olc 723	. . . . . . . . 9 $\/$
9	8	adantl 277	. . . . . . . 8 $/\$ $\/$
10	9	orcd 745	. . . . . . 7 $/\$ $\/$ $\/$ $\/$
11	10, 4	sylibr 134	. . . . . 6 $/\$ DECID $\/$
12		ioran 764	. . . . . . . . 9 $\/$ $/\$
13	12	biimpri 133	. . . . . . . 8 $/\$ $\/$
14	13	olcd 746	. . . . . . 7 $/\$ $\/$ $\/$ $\/$
15	14, 4	sylibr 134	. . . . . 6 $/\$ DECID $\/$
16	11, 15	jaodan 809	. . . . 5 $/\$ $\/$ DECID $\/$
17	7, 16	sylan2b 287	. . . 4 $/\$ DECID DECID $\/$
18	17	ex 115	. . 3 DECID DECID $\/$
19	6, 18	jaoi 728	. 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 720 DECID wdc 846

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 623 ax-in2 624 ax-io 721

This theorem depends on definitions: df-bi 117 df-dc 847

This theorem is referenced by: pm4.55dc 951 orandc 952 pm3.12dc 971 pm3.13dc 972 dn1dc 973 eueq3dc 3000 distrlem4prl 7941 distrlem4pru 7942 exfzdc 10637 lcmmndc 12818 isprm3 12874 perfectlem2 16028 lgsval 16037 lgsfvalg 16038 lgsfcl2 16039 lgsval2lem 16043 lgsdir2 16066 lgsne0 16071 lgsdirnn0 16080 lgsdinn0 16081 2lgs 16137 2lgsoddprm 16146 eupth2lem3lem4fi 16628 eupth2lem3lem7fi 16629 cndcap 17014