pm3.13dc - Intuitionistic Logic Explorer

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Theorem pm3.13dc 949

Description: Theorem *3.13 of [WhiteheadRussell] p. 111, but for decidable propositions. The converse, pm3.14 743, holds for all propositions. (Contributed by Jim Kingdon, 22-Apr-2018.)

**Assertion**
Ref	Expression
pm3.13dc	DECID DECID $/\$ $\/$

**Proof of Theorem pm3.13dc**
Step	Hyp	Ref	Expression
1		dcn 832	. . 3 DECID DECID
2		dcn 832	. . 3 DECID DECID
3		dcor 925	. . 3 DECID DECID DECID $\/$
4	1, 2, 3	syl2im 38	. 2 DECID DECID DECID $\/$
5		pm3.11dc 947	. 2 DECID DECID $\/$ $/\$
6		con1dc 846	. 2 DECID $\/$ $\/$ $/\$ $/\$ $\/$
7	4, 5, 6	syl6c 66	1 DECID DECID $/\$ $\/$

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $/\$ wa 103 $\/$ wo 698 DECID wdc 824

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 604 ax-in2 605 ax-io 699

This theorem depends on definitions: df-bi 116 df-stab 821 df-dc 825

This theorem is referenced by: (None)

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