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Theorem uniprg 3906

Description: The union of a pair is the union of its members. Proposition 5.7 of [TakeutiZaring] p. 16. (Contributed by NM, 25-Aug-2006.)

**Assertion**
Ref	Expression
uniprg	$/\$

Proof of Theorem uniprg Dummy variables

are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		preq1 3799	. . . 4
2	1	unieqd 3902	. . 3
3		uneq1 3411	. . 3
4	2, 3	eqeq12d 2367	. 2
5		preq2 3800	. . . 4
6	5	unieqd 3902	. . 3
7		uneq2 3412	. . 3
8	6, 7	eqeq12d 2367	. 2
9		vex 2862	. . 3
10		vex 2862	. . 3
11	9, 10	unipr 3905	. 2
12	4, 8, 11	vtocl2g 2918	1 $/\$

Colors of variables: wff setvar class

Syntax hints:

wi 4 $/\$ wa 358

wceq 1642

wcel 1710

cun 3207

cpr 3738

cuni 3891

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334

This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-rex 2620 df-v 2861 df-nin 3211 df-compl 3212 df-un 3214 df-sn 3741 df-pr 3742 df-uni 3892

This theorem is referenced by: (None)