Theorem nfixp1 7509

Description: The index variable in an indexed Cartesian 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.

Step	Hyp	Ref	Expression
1		df-ixp 7490	. 2
2		nfcv 2619	. . . . 5
3		nfab1 2621	. . . . 5
4	2, 3	nffn 5682	. . . 4
5		nfra1 2838	. . . 4
6	4, 5	nfan 1928	. . 3
7	6	nfab 2623	. 2
8	1, 7	nfcxfr 2617	1

Syntax hints:  /\wa 369  e.wcel 1818  {cab 2442  F/_wnfc 2605  A.wral 2807  Fnwfn 5588  `cfv 5593  X_cixp 7489

This theorem is referenced by:  ixpiunwdom  8038  ptbasfi  20082

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-fun 5595  df-fn 5596  df-ixp 7490