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Theorem unopab 2676

Description: Union of two ordered pair class abstractions.

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

**Proof of Theorem unopab**
Step	Hyp	Ref	Expression
1		unab 2265	. . 3 $/\$ $/\$ $/\$ $\/$ $/\$
2		19.43 1087	. . . . 5 $/\$ $\/$ $/\$ $/\$ $\/$ $/\$
3		andi 603	. . . . . . . 8 $/\$ $\/$ $/\$ $\/$ $/\$
4	3	exbii 1050	. . . . . . 7 $/\$ $\/$ $/\$ $\/$ $/\$
5		19.43 1087	. . . . . . 7 $/\$ $\/$ $/\$ $/\$ $\/$ $/\$
6	4, 5	bitr2 174	. . . . . 6 $/\$ $\/$ $/\$ $/\$ $\/$
7	6	exbii 1050	. . . . 5 $/\$ $\/$ $/\$ $/\$ $\/$
8	2, 7	bitr3 175	. . . 4 $/\$ $\/$ $/\$ $/\$ $\/$
9	8	abbii 1574	. . 3 $/\$ $\/$ $/\$ $/\$ $\/$
10	1, 9	eqtr 1494	. 2 $/\$ $/\$ $/\$ $\/$
11		df-opab 2664	. . 3 $/\$
12		df-opab 2664	. . 3 $/\$
13	11, 12	uneq12i 2180	. 2 $/\$ $/\$
14		df-opab 2664	. 2 $\/$ $/\$ $\/$
15	10, 13, 14	3eqtr4 1504	1 $\/$

Colors of variables: wff set class

Syntax hints: $\/$ wo 222 $/\$ wa 223

wceq 955

wex 979

cab 1463

cun 2043

cop 2409

copab 2663

This theorem is referenced by: xpundi 3222 xpundir 3223 fopabap 3838

This theorem was proved from axioms: ax-1 4 ax-2 5 ax-3 6 ax-mp 7 ax-7 961 ax-gen 962 ax-8 963 ax-10 965 ax-12 967 ax-17 970 ax-4 972 ax-5o 974 ax-6o 977 ax-9o 1122 ax-10o 1139 ax-16 1210 ax-11o 1218 ax-ext 1459

This theorem depends on definitions: df-bi 147 df-or 224 df-an 225 df-ex 980 df-sb 1172 df-clab 1464 df-cleq 1469 df-clel 1472 df-v 1810 df-un 2048 df-opab 2664