pm5.24dc - Intuitionistic Logic Explorer

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Theorem pm5.24dc 1376

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 1375	. . . . 5 DECID DECID $/\$ $\/$ $/\$
2	1	imp 123	. . . 4 DECID $/\$ DECID $/\$ $\/$ $/\$
3	2	notbid 656	. . 3 DECID $/\$ DECID $/\$ $\/$ $/\$
4		xordc 1370	. . . 4 DECID DECID $/\$ $\/$ $/\$
5	4	imp 123	. . 3 DECID $/\$ DECID $/\$ $\/$ $/\$
6	3, 5	bitr3d 189	. 2 DECID $/\$ DECID $/\$ $\/$ $/\$ $/\$ $\/$ $/\$
7	6	ex 114	1 DECID DECID $/\$ $\/$ $/\$ $/\$ $\/$ $/\$

Colors of variables: wff set class

Syntax hints:

wn 3

wi 4 $/\$ wa 103

wb 104 $\/$ wo 697 DECID wdc 819

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 603 ax-in2 604 ax-io 698

This theorem depends on definitions: df-bi 116 df-stab 816 df-dc 820 df-xor 1354

This theorem is referenced by: (None)