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Theorem evlf2val 14969
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 14968 . 2
14 simprl 740 . . . 4
1514fveq1d 5663 . . 3
16 simprr 741 . . . 4
1716fveq2d 5665 . . 3
1815, 17oveq12d 6079 . 2
19 evlf2val.a . 2
20 evlf2val.k . 2
21 ovex 6086 . . 3
2221a1i 11 . 2
2313, 18, 19, 20, 22ovmpt2d 6188 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 362  =wceq 1687  e.wcel 1749   cvv 2951  <.cop 3856  `cfv 5390  (class class class)co 6061   c1st 6544   c2nd 6545   cbs 14114   chom 14189   cco 14190   ccat 14542   cfunc 14704   cnat 14791   cevlf 14959
This theorem is referenced by:  evlfcllem  14971  evlfcl  14972  uncf2  14987  yonedalem3b  15029
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1586  ax-4 1597  ax-5 1661  ax-6 1701  ax-7 1721  ax-8 1751  ax-9 1753  ax-10 1768  ax-11 1773  ax-12 1785  ax-13 1934  ax-ext 2403  ax-rep 4378  ax-sep 4388  ax-nul 4396  ax-pow 4442  ax-pr 4503  ax-un 6342
This theorem depends on definitions:  df-bi 179  df-or 363  df-an 364  df-3an 952  df-tru 1355  df-ex 1582  df-nf 1585  df-sb 1694  df-eu 2248  df-mo 2249  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2547  df-ne 2587  df-ral 2699  df-rex 2700  df-reu 2701  df-rab 2703  df-v 2953  df-sbc 3165  df-csb 3266  df-dif 3308  df-un 3310  df-in 3312  df-ss 3319  df-nul 3615  df-if 3769  df-pw 3839  df-sn 3859  df-pr 3860  df-op 3862  df-uni 4067  df-iun 4148  df-br 4268  df-opab 4326  df-mpt 4327  df-id 4607  df-xp 4817  df-rel 4818  df-cnv 4819  df-co 4820  df-dm 4821  df-rn 4822  df-res 4823  df-ima 4824  df-iota 5353  df-fun 5392  df-fn 5393  df-f 5394  df-f1 5395  df-fo 5396  df-f1o 5397  df-fv 5398  df-ov 6064  df-oprab 6065  df-mpt2 6066  df-1st 6546  df-2nd 6547  df-evlf 14963
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