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Theorem csbresg 4615
 Description: Distribute proper substitution through the restriction of a class. (Contributed by Alan Sare, 10-Nov-2012.)
Assertion
Ref Expression
csbresg

Proof of Theorem csbresg
StepHypRef Expression
1 csbing 3144 . . 3
2 csbxpg 4421 . . . . 5
3 csbconstg 2864 . . . . . 6
43xpeq2d 4369 . . . . 5
52, 4eqtrd 2072 . . . 4
65ineq2d 3138 . . 3
71, 6eqtrd 2072 . 2
8 df-res 4357 . . 3
98csbeq2i 2876 . 2
10 df-res 4357 . 2
117, 9, 103eqtr4g 2097 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1243   wcel 1393  cvv 2557  csb 2852   cin 2916   cxp 4343   cres 4347 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rab 2315  df-v 2559  df-sbc 2765  df-csb 2853  df-in 2924  df-opab 3819  df-xp 4351  df-res 4357 This theorem is referenced by: (None)
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