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Theorem evlf2val 15362
 Description: Value of the evaluation natural transformation at an object. (Contributed by Mario Carneiro, 12-Jan-2017.)
Hypotheses
Ref Expression
evlfval.e evalF
evlfval.c
evlfval.d
evlfval.b
evlfval.h
evlfval.o comp
evlfval.n Nat
evlf2.f
evlf2.g
evlf2.x
evlf2.y
evlf2.l
evlf2val.a
evlf2val.k
Assertion
Ref Expression
evlf2val

Proof of Theorem evlf2val
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 evlfval.e . . 3 evalF
2 evlfval.c . . 3
3 evlfval.d . . 3
4 evlfval.b . . 3
5 evlfval.h . . 3
6 evlfval.o . . 3 comp
7 evlfval.n . . 3 Nat
8 evlf2.f . . 3
9 evlf2.g . . 3
10 evlf2.x . . 3
11 evlf2.y . . 3
12 evlf2.l . . 3
131, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12evlf2 15361 . 2
14 simprl 755 . . . 4
1514fveq1d 5874 . . 3
16 simprr 756 . . . 4
1716fveq2d 5876 . . 3
1815, 17oveq12d 6313 . 2
19 evlf2val.a . 2
20 evlf2val.k . 2
21 ovex 6320 . . 3
2221a1i 11 . 2
2313, 18, 19, 20, 22ovmpt2d 6425 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   wceq 1379   wcel 1767  cvv 3118  cop 4039  cfv 5594  (class class class)co 6295  c1st 6793  c2nd 6794  cbs 14506   chom 14582  compcco 14583  ccat 14935   cfunc 15097   Nat cnat 15184   evalF cevlf 15352 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-8 1769  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-rep 4564  ax-sep 4574  ax-nul 4582  ax-pow 4631  ax-pr 4692  ax-un 6587 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2822  df-rex 2823  df-reu 2824  df-rab 2826  df-v 3120  df-sbc 3337  df-csb 3441  df-dif 3484  df-un 3486  df-in 3488  df-ss 3495  df-nul 3791  df-if 3946  df-pw 4018  df-sn 4034  df-pr 4036  df-op 4040  df-uni 4252  df-iun 4333  df-br 4454  df-opab 4512  df-mpt 4513  df-id 4801  df-xp 5011  df-rel 5012  df-cnv 5013  df-co 5014  df-dm 5015  df-rn 5016  df-res 5017  df-ima 5018  df-iota 5557  df-fun 5596  df-fn 5597  df-f 5598  df-f1 5599  df-fo 5600  df-f1o 5601  df-fv 5602  df-ov 6298  df-oprab 6299  df-mpt2 6300  df-1st 6795  df-2nd 6796  df-evlf 15356 This theorem is referenced by:  evlfcllem  15364  evlfcl  15365  uncf2  15380  yonedalem3b  15422
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