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Theorem csbco3g 3058
 Description: Composition of two class substitutions. (Contributed by NM, 27-Nov-2005.) (Revised by Mario Carneiro, 11-Nov-2016.)
Hypothesis
Ref Expression
sbcco3g.1
Assertion
Ref Expression
csbco3g
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   (,)   ()   ()   (,)

Proof of Theorem csbco3g
StepHypRef Expression
1 csbnestg 3054 . 2
2 elex 2697 . . . 4
3 nfcvd 2282 . . . . 5
4 sbcco3g.1 . . . . 5
53, 4csbiegf 3043 . . . 4
62, 5syl 14 . . 3
76csbeq1d 3010 . 2
81, 7eqtrd 2172 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1331   wcel 1480  cvv 2686  csb 3003 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-sbc 2910  df-csb 3004 This theorem is referenced by: (None)
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