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Theorem unss1 3432

Description: Subclass law for union of classes. (Contributed by NM, 14-Oct-1999.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)

**Assertion**
Ref	Expression
unss1

Proof of Theorem unss1 Dummy variable

is distinct from all other variables.

Step	Hyp	Ref	Expression
1		ssel 3267	. . . 4
2	1	orim1d 812	. . 3 $\/$ $\/$
3		elun 3220	. . 3 $\/$
4		elun 3220	. . 3 $\/$
5	2, 3, 4	3imtr4g 261	. 2
6	5	ssrdv 3278	1

Colors of variables: wff setvar class

Syntax hints:

wi 4 $\/$ wo 357

wcel 1710

cun 3207

wss 3257

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-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-ss 3259

This theorem is referenced by: unss2 3434 unss12 3435 pwadjoin 4119