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Theorem prodex 13714
Description: A product is a set. (Contributed by Scott Fenton, 4-Dec-2017.)
Assertion
Ref Expression
prodex

Proof of Theorem prodex
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-prod 13713 . 2
2 iotaex 5573 . 2
31, 2eqeltri 2541 1
Colors of variables: wff setvar class
Syntax hints:  \/wo 368  /\wa 369  /\w3a 973  =wceq 1395  E.wex 1612  e.wcel 1818  =/=wne 2652  E.wrex 2808   cvv 3109  [_csb 3434  C_wss 3475  ifcif 3941   class class class wbr 4452  e.cmpt 4510  iotacio 5554  -1-1-onto->wf1o 5592  `cfv 5593  (class class class)co 6296  0cc0 9513  1c1 9514   cmul 9518   cn 10561   cz 10889   cuz 11110   cfz 11701  seqcseq 12107   cli 13307  prod_cprod 13712
This theorem is referenced by:  risefacval  29130  fallfacval  29131  etransclem13  32030
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  ax-nul 4581
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-v 3111  df-sbc 3328  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-sn 4030  df-pr 4032  df-uni 4250  df-iota 5556  df-prod 13713
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