excxor - Intuitionistic Logic Explorer

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Theorem excxor 1389

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 1388	. . 3 $\/_$ $\/$ $/\$ $\/$
2		andi 819	. . 3 $\/$ $/\$ $\/$ $\/$ $/\$ $\/$ $\/$ $/\$
3		orcom 729	. . . . 5 $/\$ $\/$ $/\$ $/\$ $\/$ $/\$
4		pm3.24 694	. . . . . 6 $/\$
5	4	biorfi 747	. . . . 5 $/\$ $/\$ $\/$ $/\$
6		andir 820	. . . . 5 $\/$ $/\$ $/\$ $\/$ $/\$
7	3, 5, 6	3bitr4ri 213	. . . 4 $\/$ $/\$ $/\$
8		pm5.61 795	. . . 4 $\/$ $/\$ $/\$
9	7, 8	orbi12i 765	. . 3 $\/$ $/\$ $\/$ $\/$ $/\$ $/\$ $\/$ $/\$
10	1, 2, 9	3bitri 206	. 2 $\/_$ $/\$ $\/$ $/\$
11		orcom 729	. 2 $/\$ $\/$ $/\$ $/\$ $\/$ $/\$
12		ancom 266	. . 3 $/\$ $/\$
13	12	orbi2i 763	. 2 $/\$ $\/$ $/\$ $/\$ $\/$ $/\$
14	10, 11, 13	3bitri 206	1 $\/_$ $/\$ $\/$ $/\$

Colors of variables: wff set class

Syntax hints:

wn 3 $/\$ wa 104

wb 105 $\/$ wo 709 $\/_$ wxo 1386

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-xor 1387

This theorem is referenced by: xordc 1403 symdifxor 3429