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Theorem sbcco3g 3307
 Description: Composition of two substitutions. (Contributed by NM, 27-Nov-2005.) (Revised by Mario Carneiro, 11-Nov-2016.)
Hypothesis
Ref Expression
sbcco3g.1
Assertion
Ref Expression
sbcco3g
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()   (,)   ()   (,)

Proof of Theorem sbcco3g
StepHypRef Expression
1 sbcnestg 3302 . 2
2 elex 2966 . . 3
3 nfcvd 2575 . . . 4
4 sbcco3g.1 . . . 4
53, 4csbiegf 3293 . . 3
6 dfsbcq 3165 . . 3
72, 5, 63syl 19 . 2
81, 7bitrd 246 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wceq 1653   wcel 1726  cvv 2958  wsbc 3163  csb 3253 This theorem is referenced by:  sbcco3gOLD  3308 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-sbc 3164  df-csb 3254
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