stdcndcOLD - Intuitionistic Logic Explorer

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Theorem stdcndcOLD 841

Description: Obsolete version of stdcndc 840 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 831	. . . . . 6 DECID $\/$
2	1	adantl 275	. . . . 5 STAB $/\$ DECID $\/$
3		df-stab 826	. . . . . . . 8 STAB
4	3	biimpi 119	. . . . . . 7 STAB
5	4	orim2d 783	. . . . . 6 STAB $\/$ $\/$
6	5	adantr 274	. . . . 5 STAB $/\$ DECID $\/$ $\/$
7	2, 6	mpd 13	. . . 4 STAB $/\$ DECID $\/$
8	7	orcomd 724	. . 3 STAB $/\$ DECID $\/$
9		df-dc 830	. . 3 DECID $\/$
10	8, 9	sylibr 133	. 2 STAB $/\$ DECID DECID
11		dcstab 839	. . 3 DECID STAB
12		dcn 837	. . 3 DECID DECID
13	11, 12	jca 304	. 2 DECID STAB $/\$ DECID
14	10, 13	impbii 125	1 STAB $/\$ DECID DECID

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $/\$ wa 103

wb 104 $\/$ wo 703 STAB wstab 825 DECID wdc 829

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 609 ax-in2 610 ax-io 704

This theorem depends on definitions: df-bi 116 df-stab 826 df-dc 830

This theorem is referenced by: (None)

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