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Theorem sbcco2 2846
 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 2828 . 2
2 nfv 1462 . . 3
3 sbcco2.1 . . . . 5
43equcoms 1636 . . . 4
5 dfsbcq 2826 . . . . 5
65bicomd 139 . . . 4
74, 6syl 14 . . 3
82, 7sbie 1716 . 2
91, 8bitr3i 184 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103   wceq 1285  wsb 1687  wsbc 2824 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-sbc 2825 This theorem is referenced by: (None)
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