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Theorem nfopab1 4518
 Description: The first 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
nfopab1

Proof of Theorem nfopab1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-opab 4511 . 2
2 nfe1 1840 . . 3
32nfab 2623 . 2
41, 3nfcxfr 2617 1
 Colors of variables: wff setvar class Syntax hints:  /\wa 369  =wceq 1395  E.wex 1612  {cab 2442  F/_wnfc 2605  <.cop 4035  {copab 4509 This theorem is referenced by:  nfmpt1  4541  opelopabsb  4762  ssopab2b  4779  dmopab  5218  rnopab  5252  funopab  5626  fvopab5  5979  0neqopab  6341  zfrep6  6768  opabdm  27464  opabrn  27465  fpwrelmap  27556  aomclem8  31007 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-opab 4511
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