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Theorem fconstg 5777
Description: A Cartesian product with a singleton is a constant function. (Contributed by NM, 19-Oct-2004.)
Assertion
Ref Expression
fconstg

Proof of Theorem fconstg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sneq 4039 . . . 4
21xpeq2d 5028 . . 3
3 feq1 5718 . . . 4
4 feq3 5720 . . . 4
53, 4sylan9bb 699 . . 3
62, 1, 5syl2anc 661 . 2
7 vex 3112 . . 3
87fconst 5776 . 2
96, 8vtoclg 3167 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  e.wcel 1818  {csn 4029  X.cxp 5002  -->wf 5589
This theorem is referenced by:  fnconstg  5778  fconst6g  5779  xpsng  6072  fvconst2g  6124  fconst2g  6125  xkoptsub  20155  mbfconstlem  22036  i1fmulclem  22109  i1fmulc  22110  itg2mulclem  22153  dvcmulf  22348  dvef  22381  coemulc  22652  resf1o  27553  locfinref  27844  ccatmulgnn0dir  28496
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-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
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-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  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-mpt 4512  df-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-rn 5015  df-fun 5595  df-fn 5596  df-f 5597
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