pm3.12dc - Intuitionistic Logic Explorer

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Theorem pm3.12dc 865

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 864	. . . 4 DECID DECID $\/$ $/\$
2	1	imp 115	. . 3 DECID $/\$ DECID $\/$ $/\$
3		dcn 746	. . . . . 6 DECID DECID
4		dcn 746	. . . . . 6 DECID DECID
5		dcor 843	. . . . . 6 DECID DECID DECID $\/$
6	3, 4, 5	syl2im 34	. . . . 5 DECID DECID DECID $\/$
7		dfordc 791	. . . . 5 DECID $\/$ $\/$ $\/$ $/\$ $\/$ $/\$
8	6, 7	syl6 29	. . . 4 DECID DECID $\/$ $\/$ $/\$ $\/$ $/\$
9	8	imp 115	. . 3 DECID $/\$ DECID $\/$ $\/$ $/\$ $\/$ $/\$
10	2, 9	mpbird 156	. 2 DECID $/\$ DECID $\/$ $\/$ $/\$
11	10	ex 108	1 DECID DECID $\/$ $\/$ $/\$

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $/\$ wa 97

wb 98 $\/$ wo 629 DECID wdc 742

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630

This theorem depends on definitions: df-bi 110 df-dc 743

This theorem is referenced by: (None)