testbitestn - Intuitionistic Logic Explorer

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Theorem testbitestn 861

Description: A proposition is testable iff its negation is testable. See also dcn 784 (which could be read as "Decidability implies testability"). (Contributed by David A. Wheeler, 6-Dec-2018.)

**Assertion**
Ref	Expression
testbitestn	DECID DECID

**Proof of Theorem testbitestn**
Step	Hyp	Ref	Expression
1		notnotnot 663	. . . 4
2	1	orbi2i 714	. . 3 $\/$ $\/$
3		orcom 682	. . 3 $\/$ $\/$
4	2, 3	bitri 182	. 2 $\/$ $\/$
5		df-dc 781	. 2 DECID $\/$
6		df-dc 781	. 2 DECID $\/$
7	4, 5, 6	3bitr4ri 211	1 DECID DECID

Colors of variables: wff set class

Syntax hints:

wn 3

wb 103 $\/$ wo 664 DECID wdc 780

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 579 ax-in2 580 ax-io 665

This theorem depends on definitions: df-bi 115 df-dc 781

This theorem is referenced by: (None)

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