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Theorem evlf2val 15188
 Description: Value of the evaluation natural transformation at an object. (Contributed by Mario Carneiro, 12-Jan-2017.)
Hypotheses
Ref Expression
evlfval.e
evlfval.c
evlfval.d
evlfval.b
evlfval.h
evlfval.o
evlfval.n
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
2 evlfval.c . . 3
3 evlfval.d . . 3
4 evlfval.b . . 3
5 evlfval.h . . 3
6 evlfval.o . . 3
7 evlfval.n . . 3
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 15187 . 2
14 simprl 755 . . . 4
1514fveq1d 5815 . . 3
16 simprr 756 . . . 4
1716fveq2d 5817 . . 3
1815, 17oveq12d 6240 . 2
19 evlf2val.a . 2
20 evlf2val.k . 2
21 ovex 6247 . . 3
2221a1i 11 . 2
2313, 18, 19, 20, 22ovmpt2d 6351 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  =wceq 1370  e.wcel 1758   cvv 3081  <.cop 3999  `cfv 5537  (class class class)co 6222   c1st 6708   c2nd 6709   cbs 14332   chom 14408   cco 14409   ccat 14761   cfunc 14923   cnat 15010   cevlf 15178 This theorem is referenced by:  evlfcllem  15190  evlfcl  15191  uncf2  15206  yonedalem3b  15248 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-8 1760  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432  ax-rep 4520  ax-sep 4530  ax-nul 4538  ax-pow 4587  ax-pr 4648  ax-un 6505 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2266  df-mo 2267  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-ral 2805  df-rex 2806  df-reu 2807  df-rab 2809  df-v 3083  df-sbc 3298  df-csb 3402  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3752  df-if 3906  df-pw 3978  df-sn 3994  df-pr 3996  df-op 4000  df-uni 4209  df-iun 4290  df-br 4410  df-opab 4468  df-mpt 4469  df-id 4753  df-xp 4963  df-rel 4964  df-cnv 4965  df-co 4966  df-dm 4967  df-rn 4968  df-res 4969  df-ima 4970  df-iota 5500  df-fun 5539  df-fn 5540  df-f 5541  df-f1 5542  df-fo 5543  df-f1o 5544  df-fv 5545  df-ov 6225  df-oprab 6226  df-mpt2 6227  df-1st 6710  df-2nd 6711  df-evlf 15182
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