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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
StepHypRef Expression
1 csbing 3462 . . 3
2 csbxpg 4813 . . . . 5
3 csbconstg 3150 . . . . . 6
43xpeq2d 4808 . . . . 5
52, 4eqtrd 2385 . . . 4
65ineq2d 3457 . . 3
71, 6eqtrd 2385 . 2
8 df-res 4788 . . 3
98csbeq2i 3162 . 2
10 df-res 4788 . 2
117, 9, 103eqtr4g 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-mp 5  ax-1 6  ax-2 7  ax-3 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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