pm2.13dc - Intuitionistic Logic Explorer

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Theorem pm2.13dc 779

Description: A decidable proposition or its triple negation is true. Theorem *2.13 of [WhiteheadRussell] p. 101 with decidability condition added. (Contributed by Jim Kingdon, 13-May-2018.)

**Assertion**
Ref	Expression
pm2.13dc	DECID $\/$

**Proof of Theorem pm2.13dc**
Step	Hyp	Ref	Expression
1		df-dc 743	. . 3 DECID $\/$
2		notnotrdc 751	. . . . 5 DECID
3	2	con3d 561	. . . 4 DECID
4	3	orim2d 702	. . 3 DECID $\/$ $\/$
5	1, 4	syl5bi 141	. 2 DECID DECID $\/$
6	5	pm2.43i 43	1 DECID $\/$

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $\/$ 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)

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