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Theorem imaco 4769
Description: Image of the composition of two classes. (Contributed by Jason Orendorff, 12-Dec-2006.)
Assertion
Ref Expression
imaco  o. 
" C  " " C

Proof of Theorem imaco
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-rex 2306 . . 3  " C 
" C
2 vex 2554 . . . 4 
_V
32elima 4616 . . 3  " " C  " C
4 rexcom4 2571 . . . . 5  C  C
5 r19.41v 2460 . . . . . 6  C  C
65exbii 1493 . . . . 5  C  C
74, 6bitri 173 . . . 4  C  C
82elima 4616 . . . . 5  o.  " C  C  o.
9 vex 2554 . . . . . . 7 
_V
109, 2brco 4449 . . . . . 6  o.
1110rexbii 2325 . . . . 5  C  o.  C
128, 11bitri 173 . . . 4  o.  " C  C
13 vex 2554 . . . . . . 7 
_V
1413elima 4616 . . . . . 6  " C  C
1514anbi1i 431 . . . . 5 
" C  C
1615exbii 1493 . . . 4  " C  C
177, 12, 163bitr4i 201 . . 3  o.  " C  " C
181, 3, 173bitr4ri 202 . 2  o.  " C  "
" C
1918eqriv 2034 1  o. 
" C  " " C
Colors of variables: wff set class
Syntax hints:   wa 97   wceq 1242  wex 1378   wcel 1390  wrex 2301   class class class wbr 3755   "cima 4291    o. ccom 4292
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3866  ax-pow 3918  ax-pr 3935
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-pw 3353  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756  df-opab 3810  df-xp 4294  df-cnv 4296  df-co 4297  df-dm 4298  df-rn 4299  df-res 4300  df-ima 4301
This theorem is referenced by:  fvco2  5185
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