pm3.12dc - Intuitionistic Logic Explorer

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Theorem pm3.12dc 953

Description: Theorem *3.12 of [WhiteheadRussell] p. 111, but for decidable propositions. (Contributed by Jim Kingdon, 22-Apr-2018.)

**Assertion**
Ref	Expression
pm3.12dc	DECID DECID $\/$ $\/$ $/\$

**Proof of Theorem pm3.12dc**
Step	Hyp	Ref	Expression
1		pm3.11dc 952	. . . 4 DECID DECID $\/$ $/\$
2	1	imp 123	. . 3 DECID $/\$ DECID $\/$ $/\$
3		dcn 837	. . . . . 6 DECID DECID
4		dcn 837	. . . . . 6 DECID DECID
5		dcor 930	. . . . . 6 DECID DECID DECID $\/$
6	3, 4, 5	syl2im 38	. . . . 5 DECID DECID DECID $\/$
7		dfordc 887	. . . . 5 DECID $\/$ $\/$ $\/$ $/\$ $\/$ $/\$
8	6, 7	syl6 33	. . . 4 DECID DECID $\/$ $\/$ $/\$ $\/$ $/\$
9	8	imp 123	. . 3 DECID $/\$ DECID $\/$ $\/$ $/\$ $\/$ $/\$
10	2, 9	mpbird 166	. 2 DECID $/\$ DECID $\/$ $\/$ $/\$
11	10	ex 114	1 DECID DECID $\/$ $\/$ $/\$

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $/\$ wa 103

wb 104 $\/$ wo 703 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)