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Theorem csbresg 4976

Description: Distribute proper substitution through the restriction of a class. csbresg 4976 is derived from the virtual deduction proof csbresgVD in set.mm. (Contributed by Alan Sare, 10-Nov-2012.)

**Assertion**
Ref	Expression
csbresg

**Proof of Theorem csbresg**
Step	Hyp	Ref	Expression
1		csbing 3462	. . 3
2		csbxpg 4813	. . . . 5
3		csbconstg 3150	. . . . . 6
4	3	xpeq2d 4808	. . . . 5
5	2, 4	eqtrd 2385	. . . 4
6	5	ineq2d 3457	. . 3
7	1, 6	eqtrd 2385	. 2
8		df-res 4788	. . 3
9	8	csbeq2i 3162	. 2
10		df-res 4788	. 2
11	7, 9, 10	3eqtr4g 2410	1

Colors of variables: wff setvar class

Syntax hints:

wi 4

wceq 1642

wcel 1710

cvv 2859

csb 3136

cin 3208

cxp 4770

cres 4774

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-3an 936 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-sbc 3047 df-csb 3137 df-nin 3211 df-compl 3212 df-in 3213 df-opab 4623 df-xp 4784 df-res 4788

This theorem is referenced by: (None)

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