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Theorem nfopab2 3827
 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 3819 . 2
2 nfe1 1385 . . . 4
32nfex 1528 . . 3
43nfab 2182 . 2
51, 4nfcxfr 2175 1
 Colors of variables: wff set class Syntax hints:   wa 97   wceq 1243  wex 1381  cab 2026  wnfc 2165  cop 3378  copab 3817 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-opab 3819 This theorem is referenced by:  opelopabsb  3997  ssopab2b  4013  dmopab  4546  rnopab  4581  funopab  4935  0neqopab  5550
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