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Theorem opelopabf 4037
 Description: The law of concretion. Theorem 9.5 of [Quine] p. 61. This version of opelopab 4034 uses bound-variable hypotheses in place of distinct variable conditions." (Contributed by NM, 19-Dec-2008.)
Hypotheses
Ref Expression
opelopabf.x
opelopabf.y
opelopabf.1
opelopabf.2
opelopabf.3
opelopabf.4
Assertion
Ref Expression
opelopabf
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,)   (,)   (,)

Proof of Theorem opelopabf
StepHypRef Expression
1 opelopabsb 4023 . 2
2 opelopabf.1 . . 3
3 nfcv 2220 . . . . 5
4 opelopabf.x . . . . 5
53, 4nfsbc 2836 . . . 4
6 opelopabf.3 . . . . 5
76sbcbidv 2873 . . . 4
85, 7sbciegf 2846 . . 3
92, 8ax-mp 7 . 2
10 opelopabf.2 . . 3
11 opelopabf.y . . . 4
12 opelopabf.4 . . . 4
1311, 12sbciegf 2846 . . 3
1410, 13ax-mp 7 . 2
151, 9, 143bitri 204 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103   wceq 1285  wnf 1390   wcel 1434  cvv 2602  wsbc 2816  cop 3409  copab 3846 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 3904  ax-pow 3956  ax-pr 3972 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-eu 1945  df-mo 1946  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-rex 2355  df-v 2604  df-sbc 2817  df-un 2978  df-in 2980  df-ss 2987  df-pw 3392  df-sn 3412  df-pr 3413  df-op 3415  df-opab 3848 This theorem is referenced by:  pofun  4075  fmptco  5362
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