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Theorem unopab 2753

Description: Union of two ordered pair class abstractions.

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

**Proof of Theorem unopab**
Step	Hyp	Ref	Expression
1		unab 2319	. . 3 $/\$ $/\$ $/\$ $\/$ $/\$
2		19.43 1124	. . . . 5 $/\$ $\/$ $/\$ $/\$ $\/$ $/\$
3		andi 607	. . . . . . . 8 $/\$ $\/$ $/\$ $\/$ $/\$
4	3	exbii 1087	. . . . . . 7 $/\$ $\/$ $/\$ $\/$ $/\$
5		19.43 1124	. . . . . . 7 $/\$ $\/$ $/\$ $/\$ $\/$ $/\$
6	4, 5	bitr2i 172	. . . . . 6 $/\$ $\/$ $/\$ $/\$ $\/$
7	6	exbii 1087	. . . . 5 $/\$ $\/$ $/\$ $/\$ $\/$
8	2, 7	bitr3i 173	. . . 4 $/\$ $\/$ $/\$ $/\$ $\/$
9	8	abbii 1618	. . 3 $/\$ $\/$ $/\$ $/\$ $\/$
10	1, 9	eqtri 1538	. 2 $/\$ $/\$ $/\$ $\/$
11		df-opab 2741	. . 3 $/\$
12		df-opab 2741	. . 3 $/\$
13	11, 12	uneq12i 2234	. 2 $/\$ $/\$
14		df-opab 2741	. 2 $\/$ $/\$ $\/$
15	10, 13, 14	3eqtr4i 1548	1 $\/$

Colors of variables: wff set class

Syntax hints: $\/$ wo 220 $/\$ wa 221

wceq 992

wex 1016

cab 1505

cun 2097

cop 2469

copab 2740

This theorem is referenced by: xpundi 3310 xpundir 3311 fopabap 3955

This theorem was proved from axioms: ax-1 4 ax-2 5 ax-3 6 ax-mp 7 ax-7 998 ax-gen 999 ax-8 1000 ax-10 1002 ax-12 1004 ax-17 1007 ax-4 1009 ax-5o 1011 ax-6o 1014 ax-9o 1159 ax-10o 1177 ax-16 1247 ax-11o 1255 ax-ext 1500

This theorem depends on definitions: df-bi 145 df-or 222 df-an 223 df-ex 1017 df-sb 1209 df-clab 1506 df-cleq 1511 df-clel 1514 df-v 1858 df-un 2102 df-opab 2741