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Theorem nfxp 4904
 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
nfxp.2
Assertion
Ref Expression
nfxp

Proof of Theorem nfxp
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-xp 4884 . 2
2 nfxp.1 . . . . 5
32nfcri 2566 . . . 4
4 nfxp.2 . . . . 5
54nfcri 2566 . . . 4
63, 5nfan 1846 . . 3
76nfopab 4273 . 2
81, 7nfcxfr 2569 1
 Colors of variables: wff set class Syntax hints:   wa 359   wcel 1725  wnfc 2559  copab 4265   cxp 4876 This theorem is referenced by:  opeliunxp  4929  nfres  5148  mpt2mptsx  6414  dmmpt2ssx  6416  fmpt2x  6417  ovmptss  6428  axcc2  8317  fsum2dlem  12554  fsumcom2  12558  gsumcom2  15549  prdsdsf  18397  prdsxmet  18399  fprod2dlem  25304  fprodcom2  25308  stoweidlem21  27746  stoweidlem47  27772 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-opab 4267  df-xp 4884
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