pm2.13dc - Intuitionistic Logic Explorer

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Theorem pm2.13dc 880

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 830	. . 3 DECID $\/$
2		notnotrdc 838	. . . . 5 DECID
3	2	con3d 626	. . . 4 DECID
4	3	orim2d 783	. . 3 DECID $\/$ $\/$
5	1, 4	syl5bi 151	. 2 DECID DECID $\/$
6	5	pm2.43i 49	1 DECID $\/$

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $\/$ wo 703 DECID wdc 829

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 609 ax-in2 610 ax-io 704

This theorem depends on definitions: df-bi 116 df-dc 830

This theorem is referenced by: (None)

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