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Theorem sbcco 3068
 Description: A composition law for class substitution. (Contributed by NM, 26-Sep-2003.) (Revised by Mario Carneiro, 13-Oct-2016.)
Assertion
Ref Expression
sbcco
Distinct variable group:   ,
Allowed substitution hints:   ()   (,)

Proof of Theorem sbcco
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbcex 3055 . 2
2 sbcex 3055 . 2
3 dfsbcq 3048 . . 3
4 dfsbcq 3048 . . 3
5 sbsbc 3050 . . . . . 6
65sbbii 1653 . . . . 5
7 nfv 1619 . . . . . 6
87sbco2 2086 . . . . 5
9 sbsbc 3050 . . . . 5
106, 8, 93bitr3ri 267 . . . 4
11 sbsbc 3050 . . . 4
1210, 11bitri 240 . . 3
133, 4, 12vtoclbg 2915 . 2
141, 2, 13pm5.21nii 342 1
 Colors of variables: wff setvar class Syntax hints:   wb 176  wsb 1648   wcel 1710  cvv 2859  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-or 359  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-nfc 2478  df-v 2861  df-sbc 3047 This theorem is referenced by:  sbc7  3073  sbccom  3117  sbcralt  3118  csbco  3145
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