pm2.1dc - Intuitionistic Logic Explorer

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Theorem pm2.1dc 837

Description: Commuted law of the excluded middle for a decidable proposition. Based on theorem *2.1 of [WhiteheadRussell] p. 101. (Contributed by Jim Kingdon, 25-Mar-2018.)

**Assertion**
Ref	Expression
pm2.1dc	DECID $\/$

**Proof of Theorem pm2.1dc**
Step	Hyp	Ref	Expression
1		df-dc 835	. . 3 DECID $\/$
2		orcom 728	. . 3 $\/$ $\/$
3	1, 2	bitri 184	. 2 DECID $\/$
4	3	biimpi 120	1 DECID $\/$

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $\/$ wo 708 DECID wdc 834

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-io 709

This theorem depends on definitions: df-bi 117 df-dc 835

This theorem is referenced by: pm2.6dc 862 rabrsndc 3662

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