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

Theorem opelopabf 4002
Description: The law of concretion. Theorem 9.5 of [Quine] p. 61. This version of opelopab 3999 uses bound-variable hypotheses in place of distinct variable conditions." (Contributed by NM, 19-Dec-2008.)
Hypotheses
Ref Expression
opelopabf.x  F/
opelopabf.y  F/
opelopabf.1  _V
opelopabf.2  _V
opelopabf.3
opelopabf.4
Assertion
Ref Expression
opelopabf  <. ,  >.  { <. ,  >.  |  }
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem opelopabf
StepHypRef Expression
1 opelopabsb 3988 . 2  <. ,  >.  { <. ,  >.  |  }  [.  ]. [.  ].
2 opelopabf.1 . . 3  _V
3 nfcv 2175 . . . . 5  F/_
4 opelopabf.x . . . . 5  F/
53, 4nfsbc 2778 . . . 4  F/ [.  ].
6 opelopabf.3 . . . . 5
76sbcbidv 2811 . . . 4  [.  ].  [.  ].
85, 7sbciegf 2788 . . 3  _V  [.  ].
[.  ].  [.  ].
92, 8ax-mp 7 . 2  [.  ]. [.  ].  [.  ].
10 opelopabf.2 . . 3  _V
11 opelopabf.y . . . 4  F/
12 opelopabf.4 . . . 4
1311, 12sbciegf 2788 . . 3  _V  [.  ].
1410, 13ax-mp 7 . 2  [.  ].
151, 9, 143bitri 195 1  <. ,  >.  { <. ,  >.  |  }
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98   wceq 1242   F/wnf 1346   wcel 1390   _Vcvv 2551   [.wsbc 2758   <.cop 3370   {copab 3808
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-bndl 1396  ax-4 1397  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
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-v 2553  df-sbc 2759  df-un 2916  df-in 2918  df-ss 2925  df-pw 3353  df-sn 3373  df-pr 3374  df-op 3376  df-opab 3810
This theorem is referenced by:  pofun  4040  fmptco  5273
  Copyright terms: Public domain W3C validator