Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  axpow2 Unicode version

Theorem axpow2 3957
 Description: A variant of the Axiom of Power Sets ax-pow 3955 using subset notation. Problem in {BellMachover] p. 466. (Contributed by NM, 4-Jun-2006.)
Assertion
Ref Expression
axpow2
Distinct variable group:   ,,

Proof of Theorem axpow2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ax-pow 3955 . 2
2 dfss2 2962 . . . . 5
32imbi1i 231 . . . 4
43albii 1375 . . 3
54exbii 1512 . 2
61, 5mpbir 138 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1257  wex 1397   wss 2945 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-pow 3955 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-in 2952  df-ss 2959 This theorem is referenced by:  axpow3  3958  pwex  3960
 Copyright terms: Public domain W3C validator