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Theorem pjfni 27033
 Description: Functionality of a projection. (Contributed by NM, 30-Oct-1999.) (Revised by Mario Carneiro, 23-Dec-2013.) (New usage is discouraged.)
Hypothesis
Ref Expression
pjfn.1
Assertion
Ref Expression
pjfni

Proof of Theorem pjfni
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 riotaex 6244 . 2
2 pjfn.1 . . 3
3 pjhfval 26728 . . 3
42, 3ax-mp 5 . 2
51, 4fnmpti 5692 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1405   wcel 1842  wrex 2755   cmpt 4453   wfn 5564  cfv 5569  crio 6239  (class class class)co 6278  chil 26250   cva 26251  cch 26260  cort 26261   cpjh 26268 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-9 1846  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380  ax-rep 4507  ax-sep 4517  ax-nul 4525  ax-pr 4630  ax-hilex 26330 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 976  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-eu 2242  df-mo 2243  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ne 2600  df-ral 2759  df-rex 2760  df-reu 2761  df-rab 2763  df-v 3061  df-sbc 3278  df-csb 3374  df-dif 3417  df-un 3419  df-in 3421  df-ss 3428  df-nul 3739  df-if 3886  df-sn 3973  df-pr 3975  df-op 3979  df-uni 4192  df-iun 4273  df-br 4396  df-opab 4454  df-mpt 4455  df-id 4738  df-xp 4829  df-rel 4830  df-cnv 4831  df-co 4832  df-dm 4833  df-rn 4834  df-res 4835  df-ima 4836  df-iota 5533  df-fun 5571  df-fn 5572  df-f 5573  df-f1 5574  df-fo 5575  df-f1o 5576  df-fv 5577  df-riota 6240  df-pjh 26727 This theorem is referenced by:  pjrni  27034  pjfoi  27035  pjfi  27036  dfiop2  27085  hmopidmpji  27484  pjssdif2i  27506  pjimai  27508
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