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Theorem sbcco2 3193
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 3174 . 2
2 nfv 1631 . . 3
3 sbcco2.1 . . . . 5
43equcoms 1696 . . . 4
5 dfsbcq 3172 . . . . 5
65bicomd 194 . . . 4
74, 6syl 16 . . 3
82, 7sbie 2155 . 2
91, 8bitr3i 244 1
Colors of variables: wff set class
Syntax hints:  ->wi 4  <->wb 178  =wceq 1654  [wsb 1660  [.wsbc 3170
This theorem is referenced by:  tfinds2  4884
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-11 1764  ax-12 1954  ax-ext 2424
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555  df-sb 1661  df-clab 2430  df-cleq 2436  df-clel 2439  df-sbc 3171
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