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Theorem nfdif 3192
 Description: Bound-variable hypothesis builder for class difference. (Contributed by NM, 3-Dec-2003.) (Revised by Mario Carneiro, 13-Oct-2016.)
Hypotheses
Ref Expression
nfdif.1
nfdif.2
Assertion
Ref Expression
nfdif

Proof of Theorem nfdif
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfdif2 3074 . 2
2 nfdif.2 . . . . 5
32nfcri 2273 . . . 4
43nfn 1636 . . 3
5 nfdif.1 . . 3
64, 5nfrabxy 2609 . 2
71, 6nfcxfr 2276 1
 Colors of variables: wff set class Syntax hints:   wn 3   wcel 1480  wnfc 2266  crab 2418   cdif 3063 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-rab 2423  df-dif 3068 This theorem is referenced by: (None)
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