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Theorem sbcco2 3247
 Description: A composition law for class substitution. Importantly, may occur free in the class expression substituted for . (Contributed by NM, 5-Sep-2004.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)
Hypothesis
Ref Expression
sbcco2.1
Assertion
Ref Expression
sbcco2
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()   (,)

Proof of Theorem sbcco2
StepHypRef Expression
1 sbsbc 3228 . 2
2 nfv 1647 . . 3
3 sbcco2.1 . . . . 5
43equcoms 1710 . . . 4
5 dfsbcq 3226 . . . . 5
65bicomd 194 . . . 4
74, 6syl 16 . . 3
82, 7sbie 2159 . 2
91, 8bitr3i 244 1
 Colors of variables: wff set class Syntax hints:  ->wi 4  <->wb 178  =wceq 1670  [wsb 1676  [.wsbc 3224 This theorem is referenced by:  tfinds2  6484 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1570  ax-4 1581  ax-5 1644  ax-6 1685  ax-7 1705  ax-10 1751  ax-12 1768  ax-13 1955  ax-ext 2470 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1338  df-ex 1566  df-nf 1569  df-sb 1677  df-clab 2476  df-cleq 2482  df-clel 2485  df-sbc 3225
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