Theorem avril1 4523

Description: Poisson d'Avril's Theorem. This theorem is noted for its Selbstdokumentieren property, which means, literally, "self-documenting." (Contributed by Loof Lirpa 1-Apr-04.)

Assertion

Ref	Expression
avril1	|- -. (AP~R(i` 1) /\ F(/)(0 x. 1))

Proof of Theorem avril1

Step	Hyp	Ref	Expression
1		noel 1711	. . 3 |- -. <.F, (0 x. 1)>. e. (/)
2		df-br 2063	. . 3 |- (F(/)(0 x. 1) <-> <.F, (0 x. 1)>. e. (/))
3	1, 2	mtbir 167	. 2 |- -. F(/)(0 x. 1)
4	3	intnan 516	1 |- -. (AP~R(i` 1) /\ F(/)(0 x. 1))

Syntax hints:  -. wn 1   /\ wa 196   e. wcel 1092  (/)c0 1707  P~cpw 1798  <.cop 1810   class class class wbr 2054  ` cfv 2422  (class class class)co 3001  0cc0 4028  1c1 4029  ici 4030   x. cmulc 4032

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-v 1349  df-dif 1489  df-nul 1708  df-br 2063

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