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Theorem nfxp 4314
Description: Bound-variable hypothesis builder for cross product. (Contributed by NM, 15-Sep-2003.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
nfxp.1  F/_
nfxp.2  F/_
Assertion
Ref Expression
nfxp  F/_  X.

Proof of Theorem nfxp
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-xp 4294 . 2  X.  { <. , 
>.  |  }
2 nfxp.1 . . . . 5  F/_
32nfcri 2169 . . . 4  F/
4 nfxp.2 . . . . 5  F/_
54nfcri 2169 . . . 4  F/
63, 5nfan 1454 . . 3  F/
76nfopab 3816 . 2  F/_ { <. , 
>.  |  }
81, 7nfcxfr 2172 1  F/_  X.
Colors of variables: wff set class
Syntax hints:   wa 97   wcel 1390   F/_wnfc 2162   {copab 3808    X. cxp 4286
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-opab 3810  df-xp 4294
This theorem is referenced by:  opeliunxp  4338  nfres  4557  mpt2mptsx  5765  dmmpt2ssx  5767  fmpt2x  5768
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