pm3.12dc - Intuitionistic Logic Explorer

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Theorem pm3.12dc 960

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 959	. . . 4 DECID DECID $\/$ $/\$
2	1	imp 124	. . 3 DECID $/\$ DECID $\/$ $/\$
3		dcn 843	. . . . . 6 DECID DECID
4		dcn 843	. . . . . 6 DECID DECID
5		dcor 937	. . . . . 6 DECID DECID DECID $\/$
6	3, 4, 5	syl2im 38	. . . . 5 DECID DECID DECID $\/$
7		dfordc 893	. . . . 5 DECID $\/$ $\/$ $\/$ $/\$ $\/$ $/\$
8	6, 7	syl6 33	. . . 4 DECID DECID $\/$ $\/$ $/\$ $\/$ $/\$
9	8	imp 124	. . 3 DECID $/\$ DECID $\/$ $\/$ $/\$ $\/$ $/\$
10	2, 9	mpbird 167	. 2 DECID $/\$ DECID $\/$ $\/$ $/\$
11	10	ex 115	1 DECID DECID $\/$ $\/$ $/\$

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $/\$ wa 104

wb 105 $\/$ wo 709 DECID wdc 835

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 615 ax-in2 616 ax-io 710

This theorem depends on definitions: df-bi 117 df-stab 832 df-dc 836

This theorem is referenced by: (None)