unopab - Metamath Proof Explorer

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Theorem unopab 4728

Description: Union of two ordered pair class abstractions. (Contributed by NM, 30-Sep-2002.)

**Assertion**
Ref	Expression
unopab	$\/$

Proof of Theorem unopab Dummy variable

is distinct from all other variables.

Step	Hyp	Ref	Expression
1		unab 3894	. . 3 $/\$ $/\$ $/\$ $\/$ $/\$
2		19.43 1810	. . . . 5 $/\$ $\/$ $/\$ $/\$ $\/$ $/\$
3		andi 911	. . . . . . . 8 $/\$ $\/$ $/\$ $\/$ $/\$
4	3	exbii 1774	. . . . . . 7 $/\$ $\/$ $/\$ $\/$ $/\$
5		19.43 1810	. . . . . . 7 $/\$ $\/$ $/\$ $/\$ $\/$ $/\$
6	4, 5	bitr2i 265	. . . . . 6 $/\$ $\/$ $/\$ $/\$ $\/$
7	6	exbii 1774	. . . . 5 $/\$ $\/$ $/\$ $/\$ $\/$
8	2, 7	bitr3i 266	. . . 4 $/\$ $\/$ $/\$ $/\$ $\/$
9	8	abbii 2739	. . 3 $/\$ $\/$ $/\$ $/\$ $\/$
10	1, 9	eqtri 2644	. 2 $/\$ $/\$ $/\$ $\/$
11		df-opab 4713	. . 3 $/\$
12		df-opab 4713	. . 3 $/\$
13	11, 12	uneq12i 3765	. 2 $/\$ $/\$
14		df-opab 4713	. 2 $\/$ $/\$ $\/$
15	10, 13, 14	3eqtr4i 2654	1 $\/$

Colors of variables: wff setvar class

Syntax hints: $\/$ wo 383 $/\$ wa 384

wceq 1483

wex 1704

cab 2608

cun 3572

cop 4183

copab 4712

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602

This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-un 3579 df-opab 4713

This theorem is referenced by: xpundi 5171 xpundir 5172 cnvun 5538 coundi 5636 coundir 5637 mptun 6025 opsrtoslem1 19484 lgsquadlem3 25107