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Theorem sbcrex 3012
 Description: Interchange class substitution and restricted existential quantifier. (Contributed by NM, 15-Nov-2005.) (Revised by NM, 18-Aug-2018.)
Assertion
Ref Expression
sbcrex
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)   ()   ()

Proof of Theorem sbcrex
StepHypRef Expression
1 nfcv 2296 . 2
2 sbcrext 3010 . 2
31, 2ax-mp 5 1
 Colors of variables: wff set class Syntax hints:   wb 104  wnfc 2283  wrex 2433  wsbc 2933 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-ral 2437  df-rex 2438  df-v 2711  df-sbc 2934 This theorem is referenced by:  ac6sfi  6832  rexfiuz  10866
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