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Theorem sbcco2 3069
 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 3050 . 2
2 nfv 1619 . . 3
3 sbcco2.1 . . . . 5
43eqcoms 2356 . . . 4
5 dfsbcq 3048 . . . . 5
65bicomd 192 . . . 4
74, 6syl 15 . . 3
82, 7sbie 2038 . 2
91, 8bitr3i 242 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wceq 1642  wsb 1648  wsbc 3046 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-sbc 3047 This theorem is referenced by: (None)
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