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Theorem pjhval 22904
 Description: Value of a projection. (Contributed by NM, 23-Oct-1999.) (Revised by Mario Carneiro, 15-Dec-2013.) (New usage is discouraged.)
Assertion
Ref Expression
pjhval
Distinct variable groups:   ,,   ,,

Proof of Theorem pjhval
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 pjhfval 22903 . . 3
21fveq1d 5733 . 2
3 eqeq1 2444 . . . . 5
43rexbidv 2728 . . . 4
54riotabidv 6554 . . 3
6 eqid 2438 . . 3
7 riotaex 6556 . . 3
85, 6, 7fvmpt 5809 . 2
92, 8sylan9eq 2490 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wcel 1726  wrex 2708   cmpt 4269  cfv 5457  (class class class)co 6084  crio 6545  chil 22427   cva 22428  cch 22437  cort 22438   cpjh 22445 This theorem is referenced by:  pjpreeq  22905 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-rep 4323  ax-sep 4333  ax-nul 4341  ax-pr 4406  ax-hilex 22507 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-reu 2714  df-rab 2716  df-v 2960  df-sbc 3164  df-csb 3254  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-iun 4097  df-br 4216  df-opab 4270  df-mpt 4271  df-id 4501  df-xp 4887  df-rel 4888  df-cnv 4889  df-co 4890  df-dm 4891  df-rn 4892  df-res 4893  df-ima 4894  df-iota 5421  df-fun 5459  df-fn 5460  df-f 5461  df-f1 5462  df-fo 5463  df-f1o 5464  df-fv 5465  df-riota 6552  df-pjh 22902
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