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Theorem coss1 4872

Description: Subclass theorem for composition. (Contributed by FL, 30-Dec-2010.)

**Assertion**
Ref	Expression
coss1

Proof of Theorem coss1 Dummy variables

are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		id 19	. . . . . 6
2	1	ssbrd 4680	. . . . 5
3	2	anim2d 548	. . . 4 $/\$ $/\$
4	3	eximdv 1622	. . 3 $/\$ $/\$
5	4	ssopab2dv 4715	. 2 $/\$ $/\$
6		df-co 4726	. 2 $/\$
7		df-co 4726	. 2 $/\$
8	5, 6, 7	3sstr4g 3312	1

Colors of variables: wff setvar class

Syntax hints:

wi 4 $/\$ wa 358

wex 1541

wss 3257

copab 4622 class class class wbr 4639

ccom 4721

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-ss 3259 df-opab 4623 df-br 4640 df-co 4726

This theorem is referenced by: coeq1 4874 funss 5126