stdcndcOLD - Intuitionistic Logic Explorer

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Theorem stdcndcOLD 858

Description: Obsolete version of stdcndc 857 as of 28-Oct-2023. (Contributed by David A. Wheeler, 13-Aug-2018.) (Proof modification is discouraged.) (New usage is discouraged.)

**Assertion**
Ref	Expression
stdcndcOLD	STAB $/\$ DECID DECID

**Proof of Theorem stdcndcOLD**
Step	Hyp	Ref	Expression
1		exmiddc 848	. . . . . 6 DECID $\/$
2	1	adantl 277	. . . . 5 STAB $/\$ DECID $\/$
3		df-stab 843	. . . . . . . 8 STAB
4	3	biimpi 120	. . . . . . 7 STAB
5	4	orim2d 800	. . . . . 6 STAB $\/$ $\/$
6	5	adantr 276	. . . . 5 STAB $/\$ DECID $\/$ $\/$
7	2, 6	mpd 13	. . . 4 STAB $/\$ DECID $\/$
8	7	orcomd 741	. . 3 STAB $/\$ DECID $\/$
9		df-dc 847	. . 3 DECID $\/$
10	8, 9	sylibr 134	. 2 STAB $/\$ DECID DECID
11		dcstab 856	. . 3 DECID STAB
12		dcn 854	. . 3 DECID DECID
13	11, 12	jca 306	. 2 DECID STAB $/\$ DECID
14	10, 13	impbii 126	1 STAB $/\$ DECID DECID

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $/\$ wa 104

wb 105 $\/$ wo 720 STAB wstab 842 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-stab 843 df-dc 847

This theorem is referenced by: (None)

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