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Theorem sucexg 4190
Description: The successor of a set is a set (generalization). (Contributed by NM, 5-Jun-1994.)
Assertion
Ref Expression
sucexg (A 𝑉 → suc A V)

Proof of Theorem sucexg
StepHypRef Expression
1 elex 2560 . 2 (A 𝑉A V)
2 sucexb 4189 . 2 (A V ↔ suc A V)
31, 2sylib 127 1 (A 𝑉 → suc A V)
Colors of variables: wff set class
Syntax hints:  wi 4   wcel 1390  Vcvv 2551  suc csuc 4068
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-13 1401  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3866  ax-pow 3918  ax-pr 3935  ax-un 4136
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-pw 3353  df-sn 3373  df-pr 3374  df-uni 3572  df-suc 4074
This theorem is referenced by:  sucex  4191  suceloni  4193  peano2  4261  sucinc2  5965  oav2  5982
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