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Theorem sbcco2 3176
 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 3157 . 2
2 nfv 1629 . . 3
3 sbcco2.1 . . . . 5
43equcoms 1693 . . . 4
5 dfsbcq 3155 . . . . 5
65bicomd 193 . . . 4
74, 6syl 16 . . 3
82, 7sbie 2122 . 2
91, 8bitr3i 243 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1652  wsb 1658  wsbc 3153 This theorem is referenced by:  tfinds2  4835 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-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-sbc 3154
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