New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  rspesbca Unicode version

Theorem rspesbca 3126
 Description: Existence form of rspsbca 3125. (Contributed by NM, 29-Feb-2008.) (Proof shortened by Mario Carneiro, 13-Oct-2016.)
Assertion
Ref Expression
rspesbca
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem rspesbca
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfsbcq2 3049 . . 3
21rspcev 2955 . 2
3 cbvrexsv 2847 . 2
42, 3sylibr 203 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358  wsb 1648   wcel 1710  wrex 2615  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-ral 2619  df-rex 2620  df-v 2861  df-sbc 3047 This theorem is referenced by:  spesbc  3127
 Copyright terms: Public domain W3C validator