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Theorem pgpgrp 15221
 Description: Reverse closure for the second argument of pGrp. (Contributed by Mario Carneiro, 15-Jan-2015.)
Assertion
Ref Expression
pgpgrp pGrp

Proof of Theorem pgpgrp
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eqid 2436 . . 3
2 eqid 2436 . . 3
31, 2ispgp 15219 . 2 pGrp
43simp2bi 973 1 pGrp
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  wral 2698  wrex 2699   class class class wbr 4205  cfv 5447  (class class class)co 6074  cn0 10214  cexp 11375  cprime 13072  cbs 13462  cgrp 14678  cod 15156   pGrp cpgp 15158 This theorem is referenced by:  pgphash  15234 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4323  ax-nul 4331  ax-pr 4396 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2703  df-rex 2704  df-rab 2707  df-v 2951  df-dif 3316  df-un 3318  df-in 3320  df-ss 3327  df-nul 3622  df-if 3733  df-sn 3813  df-pr 3814  df-op 3816  df-uni 4009  df-br 4206  df-opab 4260  df-xp 4877  df-iota 5411  df-fv 5455  df-ov 6077  df-pgp 15162
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