pm5.24dc - Intuitionistic Logic Explorer

	Intuitionistic Logic Explorer		< Previous Next > Nearby theorems
Mirrors > Home > ILE Home > Th. List > pm5.24dc		Unicode version

Theorem pm5.24dc 1289

Description: Theorem *5.24 of [WhiteheadRussell] p. 124, but for decidable propositions. (Contributed by Jim Kingdon, 5-May-2018.)

**Assertion**
Ref	Expression
pm5.24dc	DECID DECID $/\$ $\/$ $/\$ $/\$ $\/$ $/\$

**Proof of Theorem pm5.24dc**
Step	Hyp	Ref	Expression
1		dfbi3dc 1288	. . . . 5 DECID DECID $/\$ $\/$ $/\$
2	1	imp 115	. . . 4 DECID $/\$ DECID $/\$ $\/$ $/\$
3	2	notbid 592	. . 3 DECID $/\$ DECID $/\$ $\/$ $/\$
4		xordc 1283	. . . 4 DECID DECID $/\$ $\/$ $/\$
5	4	imp 115	. . 3 DECID $/\$ DECID $/\$ $\/$ $/\$
6	3, 5	bitr3d 179	. 2 DECID $/\$ DECID $/\$ $\/$ $/\$ $/\$ $\/$ $/\$
7	6	ex 108	1 DECID DECID $/\$ $\/$ $/\$ $/\$ $\/$ $/\$

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $/\$ wa 97

wb 98 $\/$ 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 df-xor 1267

This theorem is referenced by: (None)