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Theorem csbco3g 3307
 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 3301 . 2
2 elex 2964 . . . 4
3 nfcvd 2573 . . . . 5
4 sbcco3g.1 . . . . 5
53, 4csbiegf 3291 . . . 4
62, 5syl 16 . . 3
76csbeq1d 3257 . 2
81, 7eqtrd 2468 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  cvv 2956  csb 3251 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-sbc 3162  df-csb 3252
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