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Theorem sbcalg 3039
 Description: Move universal quantifier in and out of class substitution. (Contributed by NM, 16-Jan-2004.)
Assertion
Ref Expression
sbcalg
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   ()   (,)

Proof of Theorem sbcalg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfsbcq2 2994 . 2
2 dfsbcq2 2994 . . 3
32albidv 1611 . 2
4 sbal 2066 . 2
51, 3, 4vtoclbg 2844 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176  wal 1527   wceq 1623  wsb 1629   wcel 1684  wsbc 2991 This theorem is referenced by:  sbcabel  3068  sbcss  3564  trsbc  28304  sbcssOLD  28306  trsbcVD  28653  sbcssVD  28659  bnj89  28747  bnj538  28769  bnj611  28950  bnj1000  28973 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-sbc 2992
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