excxor - Intuitionistic Logic Explorer

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

Theorem excxor 1309

Description: This tautology shows that xor is really exclusive. (Contributed by FL, 22-Nov-2010.) (Proof rewritten by Jim Kingdon, 5-May-2018.)

**Assertion**
Ref	Expression
excxor	$\/_$ $/\$ $\/$ $/\$

**Proof of Theorem excxor**
Step	Hyp	Ref	Expression
1		xoranor 1308	. . 3 $\/_$ $\/$ $/\$ $\/$
2		andi 764	. . 3 $\/$ $/\$ $\/$ $\/$ $/\$ $\/$ $\/$ $/\$
3		orcom 679	. . . . 5 $/\$ $\/$ $/\$ $/\$ $\/$ $/\$
4		pm3.24 659	. . . . . 6 $/\$
5	4	biorfi 697	. . . . 5 $/\$ $/\$ $\/$ $/\$
6		andir 765	. . . . 5 $\/$ $/\$ $/\$ $\/$ $/\$
7	3, 5, 6	3bitr4ri 211	. . . 4 $\/$ $/\$ $/\$
8		pm5.61 740	. . . 4 $\/$ $/\$ $/\$
9	7, 8	orbi12i 713	. . 3 $\/$ $/\$ $\/$ $\/$ $/\$ $/\$ $\/$ $/\$
10	1, 2, 9	3bitri 204	. 2 $\/_$ $/\$ $\/$ $/\$
11		orcom 679	. 2 $/\$ $\/$ $/\$ $/\$ $\/$ $/\$
12		ancom 262	. . 3 $/\$ $/\$
13	12	orbi2i 711	. 2 $/\$ $\/$ $/\$ $/\$ $\/$ $/\$
14	10, 11, 13	3bitri 204	1 $\/_$ $/\$ $\/$ $/\$

Colors of variables: wff set class

Syntax hints:

wn 3 $/\$ wa 102

wb 103 $\/$ wo 661 $\/_$ wxo 1306

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 576 ax-in2 577 ax-io 662

This theorem depends on definitions: df-bi 115 df-xor 1307

This theorem is referenced by: xordc 1323 symdifxor 3230