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Theorem unab 3521

Description: Union of two class abstractions. (Contributed by NM, 29-Sep-2002.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)

**Assertion**
Ref	Expression
unab	$\/$

Proof of Theorem unab Dummy variable

is distinct from all other variables.

Step	Hyp	Ref	Expression
1		sbor 2066	. . 3 $\/$ $\/$
2		df-clab 2340	. . 3 $\/$ $\/$
3		df-clab 2340	. . . 4
4		df-clab 2340	. . . 4
5	3, 4	orbi12i 507	. . 3 $\/$ $\/$
6	1, 2, 5	3bitr4ri 269	. 2 $\/$ $\/$
7	6	uneqri 3406	1 $\/$

Colors of variables: wff setvar class

Syntax hints: $\/$ wo 357

wceq 1642

wsb 1648

wcel 1710

cab 2339

cun 3207

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-un 3214

This theorem is referenced by: unrab 3526 rabun2 3534 dfif6 3665 nnc0suc 4412 nncaddccl 4419 preaddccan2lem1 4454 ltfintrilem1 4465 nnadjoin 4520 tfinnn 4534 phiun 4614 unopab 4638 clos1basesuc 5882 leconnnc 6218 addccan2nclem2 6264 nchoicelem16 6304