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Theorem opelopabf 4226
 Description: The law of concretion. Theorem 9.5 of [Quine] p. 61. This version of opelopab 4223 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 4212 . 2
2 opelopabf.1 . . 3
3 nfcv 2392 . . . . 5
4 opelopabf.x . . . . 5
53, 4nfsbc 2956 . . . 4
6 opelopabf.3 . . . . 5
76sbcbidv 2989 . . . 4
85, 7sbciegf 2966 . . 3
92, 8ax-mp 10 . 2
10 opelopabf.2 . . 3
11 opelopabf.y . . . 4
12 opelopabf.4 . . . 4
1311, 12sbciegf 2966 . . 3
1410, 13ax-mp 10 . 2
151, 9, 143bitri 264 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178  wnf 1539   wceq 1619   wcel 1621  cvv 2740  wsbc 2935  cop 3584  copab 4016 This theorem is referenced by:  pofun  4267  fmptco  5590 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2237  ax-sep 4081  ax-nul 4089  ax-pr 4152 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-eu 2121  df-mo 2122  df-clab 2243  df-cleq 2249  df-clel 2252  df-nfc 2381  df-ne 2421  df-ral 2520  df-rex 2521  df-rab 2523  df-v 2742  df-sbc 2936  df-dif 3097  df-un 3099  df-in 3101  df-ss 3108  df-nul 3398  df-if 3507  df-sn 3587  df-pr 3588  df-op 3590  df-opab 4018
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