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Theorem opelopabf 4746
 Description: The law of concretion. Theorem 9.5 of [Quine] p. 61. This version of opelopab 4743 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 4731 . 2
2 opelopabf.1 . . 3
3 nfcv 2591 . . . . 5
4 opelopabf.x . . . . 5
53, 4nfsbc 3327 . . . 4
6 opelopabf.3 . . . . 5
76sbcbidv 3360 . . . 4
85, 7sbciegf 3337 . . 3
92, 8ax-mp 5 . 2
10 opelopabf.2 . . 3
11 opelopabf.y . . . 4
12 opelopabf.4 . . . 4
1311, 12sbciegf 3337 . . 3
1410, 13ax-mp 5 . 2
151, 9, 143bitri 274 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wceq 1437  wnf 1663   wcel 1870  cvv 3087  wsbc 3305  cop 4008  copab 4483 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-9 1874  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407  ax-sep 4548  ax-nul 4556  ax-pr 4661 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1790  df-eu 2270  df-mo 2271  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ne 2627  df-ral 2787  df-rex 2788  df-rab 2791  df-v 3089  df-sbc 3306  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3768  df-if 3916  df-sn 4003  df-pr 4005  df-op 4009  df-opab 4485 This theorem is referenced by:  pofun  4791  fmptco  6071  fmptcof2  28099
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