pm5.24dc - Intuitionistic Logic Explorer

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Theorem pm5.24dc 1409

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 1408	. . . . 5 DECID DECID $/\$ $\/$ $/\$
2	1	imp 124	. . . 4 DECID $/\$ DECID $/\$ $\/$ $/\$
3	2	notbid 668	. . 3 DECID $/\$ DECID $/\$ $\/$ $/\$
4		xordc 1403	. . . 4 DECID DECID $/\$ $\/$ $/\$
5	4	imp 124	. . 3 DECID $/\$ DECID $/\$ $\/$ $/\$
6	3, 5	bitr3d 190	. 2 DECID $/\$ DECID $/\$ $\/$ $/\$ $/\$ $\/$ $/\$
7	6	ex 115	1 DECID DECID $/\$ $\/$ $/\$ $/\$ $\/$ $/\$

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $/\$ wa 104

wb 105 $\/$ wo 709 DECID wdc 835

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-in1 615 ax-in2 616 ax-io 710

This theorem depends on definitions: df-bi 117 df-stab 832 df-dc 836 df-xor 1387

This theorem is referenced by: (None)