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Theorem opelopabaf 4260
 Description: The law of concretion. Theorem 9.5 of [Quine] p. 61. This version of opelopab 4258 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 4247 . 2
2 opelopabaf.1 . . 3
3 opelopabaf.2 . . 3
4 opelopabaf.x . . . 4
5 opelopabaf.y . . . 4
6 nfv 1629 . . . 4
7 opelopabaf.3 . . . 4
84, 5, 6, 7sbc2iegf 3032 . . 3
92, 3, 8mp2an 656 . 2
101, 9bitri 242 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wa 360  wnf 1539   wceq 1619   wcel 1621  cvv 2763  wsbc 2966  cop 3617  copab 4050 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 2239  ax-sep 4115  ax-nul 4123  ax-pr 4186 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 2122  df-mo 2123  df-clab 2245  df-cleq 2251  df-clel 2254  df-nfc 2383  df-ne 2423  df-ral 2523  df-rex 2524  df-rab 2527  df-v 2765  df-sbc 2967  df-dif 3130  df-un 3132  df-in 3134  df-ss 3141  df-nul 3431  df-if 3540  df-sn 3620  df-pr 3621  df-op 3623  df-opab 4052
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