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Theorem sbcal 3208
 Description: Move universal quantifier in and out of class substitution. (Contributed by NM, 31-Dec-2016.)
Assertion
Ref Expression
sbcal
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem sbcal
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbcex 3170 . 2
2 sbcex 3170 . . 3
32sps 1770 . 2
4 dfsbcq2 3164 . . 3
5 dfsbcq2 3164 . . . 4
65albidv 1635 . . 3
7 sbal 2204 . . 3
84, 6, 7vtoclbg 3012 . 2
91, 3, 8pm5.21nii 343 1
 Colors of variables: wff set class Syntax hints:   wb 177  wal 1549   wceq 1652  wsb 1658   wcel 1725  cvv 2956  wsbc 3161 This theorem is referenced by:  sbcfun  27963  bnj89  29086  bnj538  29108  bnj110  29229  bnj611  29289  bnj1000  29312 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-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-sbc 3162
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