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Theorem finxpnom 31863
 Description: Cartesian exponentiation when the exponent is not a natural number defaults to the empty set. (Contributed by ML, 24-Oct-2020.)
Assertion
Ref Expression
finxpnom

Proof of Theorem finxpnom
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 simpl 464 . . . . 5
21con3i 142 . . . 4
3 abid 2459 . . . 4
42, 3sylnibr 312 . . 3
5 df-finxp 31846 . . . 4
65eleq2i 2541 . . 3
74, 6sylnibr 312 . 2
87eq0rdv 3773 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 376   wceq 1452   wcel 1904  cab 2457  cvv 3031  c0 3722  cif 3872  cop 3965  cuni 4190   cxp 4837  cfv 5589   cmpt2 6310  com 6711  c1st 6810  crdg 7145  c1o 7193  cfinxp 31845 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-v 3033  df-dif 3393  df-in 3397  df-ss 3404  df-nul 3723  df-finxp 31846 This theorem is referenced by:  finxp00  31864
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