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Theorem opelopabaf 4010
 Description: The law of concretion. Theorem 9.5 of [Quine] p. 61. This version of opelopab 4008 uses bound-variable hypotheses in place of distinct variable conditions." (Contributed by Mario Carneiro, 19-Dec-2013.) (Proof shortened by Mario Carneiro, 18-Nov-2016.)
Hypotheses
Ref Expression
opelopabaf.x
opelopabaf.y
opelopabaf.1
opelopabaf.2
opelopabaf.3
Assertion
Ref Expression
opelopabaf
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,)   (,)

Proof of Theorem opelopabaf
StepHypRef Expression
1 opelopabsb 3997 . 2
2 opelopabaf.1 . . 3
3 opelopabaf.2 . . 3
4 opelopabaf.x . . . 4
5 opelopabaf.y . . . 4
6 nfv 1421 . . . 4
7 opelopabaf.3 . . . 4
84, 5, 6, 7sbc2iegf 2828 . . 3
92, 3, 8mp2an 402 . 2
101, 9bitri 173 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   wceq 1243  wnf 1349   wcel 1393  cvv 2557  wsbc 2764  cop 3378  copab 3817 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-pr 3944 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559  df-sbc 2765  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-opab 3819 This theorem is referenced by: (None)
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