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Theorem nfixp1 7075
 Description: The index variable in an indexed cross product is not free. (Contributed by Jeff Madsen, 19-Jun-2011.) (Revised by Mario Carneiro, 15-Oct-2016.)
Assertion
Ref Expression
nfixp1

Proof of Theorem nfixp1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-ixp 7057 . 2
2 nfcv 2572 . . . . 5
3 nfab1 2574 . . . . 5
42, 3nffn 5534 . . . 4
5 nfra1 2749 . . . 4
64, 5nfan 1846 . . 3
76nfab 2576 . 2
81, 7nfcxfr 2569 1
 Colors of variables: wff set class Syntax hints:   wa 359   wcel 1725  cab 2422  wnfc 2559  wral 2698   wfn 5442  cfv 5447  cixp 7056 This theorem is referenced by:  ixpiunwdom  7552  ptbasfi  17606 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-3an 938  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-ral 2703  df-rab 2707  df-v 2951  df-dif 3316  df-un 3318  df-in 3320  df-ss 3327  df-nul 3622  df-if 3733  df-sn 3813  df-pr 3814  df-op 3816  df-br 4206  df-opab 4260  df-rel 4878  df-cnv 4879  df-co 4880  df-dm 4881  df-fun 5449  df-fn 5450  df-ixp 7057
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