pm3.12dc - Intuitionistic Logic Explorer

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Theorem pm3.12dc 899

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 898	. . . 4 DECID DECID $\/$ $/\$
2	1	imp 122	. . 3 DECID $/\$ DECID $\/$ $/\$
3		dcn 779	. . . . . 6 DECID DECID
4		dcn 779	. . . . . 6 DECID DECID
5		dcor 876	. . . . . 6 DECID DECID DECID $\/$
6	3, 4, 5	syl2im 38	. . . . 5 DECID DECID DECID $\/$
7		dfordc 824	. . . . 5 DECID $\/$ $\/$ $\/$ $/\$ $\/$ $/\$
8	6, 7	syl6 33	. . . 4 DECID DECID $\/$ $\/$ $/\$ $\/$ $/\$
9	8	imp 122	. . 3 DECID $/\$ DECID $\/$ $\/$ $/\$ $\/$ $/\$
10	2, 9	mpbird 165	. 2 DECID $/\$ DECID $\/$ $\/$ $/\$
11	10	ex 113	1 DECID DECID $\/$ $\/$ $/\$

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $/\$ wa 102

wb 103 $\/$ wo 661 DECID wdc 775

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662

This theorem depends on definitions: df-bi 115 df-dc 776

This theorem is referenced by: (None)