Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  pwexg Unicode version

Theorem pwexg 3956
 Description: Power set axiom expressed in class notation, with the sethood requirement as an antecedent. Axiom 4 of [TakeutiZaring] p. 17. (Contributed by NM, 30-Oct-2003.)
Assertion
Ref Expression
pwexg

Proof of Theorem pwexg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 pweq 3387 . . 3
21eleq1d 2148 . 2
3 vex 2605 . . 3
43pwex 3955 . 2
52, 4vtoclg 2659 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1285   wcel 1434  cvv 2602  cpw 3384 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3898  ax-pow 3950 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-in 2980  df-ss 2987  df-pw 3386 This theorem is referenced by:  abssexg  3957  snexg  3958  pwel  3975  uniexb  4225  xpexg  4474  fabexg  5102  fopwdom  6370
 Copyright terms: Public domain W3C validator