Theorem isprm 14219

Description: The predicate "is a prime number". A prime number is a positive integer with exactly two positive divisors. (Contributed by Paul Chapman, 22-Jun-2011.)

Assertion

Ref	Expression
isprm

Distinct variable group:   P,

Proof of Theorem isprm

Dummy variable is distinct from all other variables.

Step	Hyp	Ref	Expression
1		breq2 4456	. . . 4
2	1	rabbidv 3101	. . 3
3	2	breq1d 4462	. 2
4		df-prm 14218	. 2
5	3, 4	elrab2 3259	1

Syntax hints:  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  {crab 2811   class class class wbr 4452  c2o 7143  cen 7533  cn 10561  cdvds 13986  cprime 14217

This theorem is referenced by:  prmnn  14220  1nprm  14222  isprm2  14225

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-prm 14218