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Theorem nfopab2 4306
 Description: The second abstraction variable in an ordered-pair class abstraction (class builder) is effectively not free. (Contributed by NM, 16-May-1995.) (Revised by Mario Carneiro, 14-Oct-2016.)
Assertion
Ref Expression
nfopab2

Proof of Theorem nfopab2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-opab 4298 . 2
2 nfe1 1750 . . . 4
32nfex 1868 . . 3
43nfab 2583 . 2
51, 4nfcxfr 2576 1
 Colors of variables: wff set class Syntax hints:   wa 360  wex 1551   wceq 1654  cab 2429  wnfc 2566  cop 3846  copab 4296 This theorem is referenced by:  opelopabsb  4500  ssopab2b  4516  dmopab  5115  rnopab  5150  funopab  5521  zfrep6  6004  0neqopab  6155  fvopab5  6570  aomclem8  27248 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-opab 4298
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