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Theorem wdomimag 8005
Description: A set is weakly dominant over its image under any function. (Contributed by Stefan O'Rear, 14-Feb-2015.) (Revised by Mario Carneiro, 25-Jun-2015.)
Assertion
Ref Expression
wdomimag  |-  ( ( Fun  F  /\  A  e.  V )  ->  ( F " A )  ~<_*  A
)

Proof of Theorem wdomimag
StepHypRef Expression
1 funimaexg 5647 . 2  |-  ( ( Fun  F  /\  A  e.  V )  ->  ( F " A )  e. 
_V )
2 wdomima2g 8004 . 2  |-  ( ( Fun  F  /\  A  e.  V  /\  ( F " A )  e. 
_V )  ->  ( F " A )  ~<_*  A
)
31, 2mpd3an3 1323 1  |-  ( ( Fun  F  /\  A  e.  V )  ->  ( F " A )  ~<_*  A
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 367    e. wcel 1823   _Vcvv 3106   class class class wbr 4439   "cima 4991   Fun wfun 5564    ~<_* cwdom 7975
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-8 1825  ax-9 1827  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432  ax-rep 4550  ax-sep 4560  ax-nul 4568  ax-pow 4615  ax-pr 4676  ax-un 6565
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 973  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-eu 2288  df-mo 2289  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2651  df-ral 2809  df-rex 2810  df-rab 2813  df-v 3108  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3784  df-if 3930  df-pw 4001  df-sn 4017  df-pr 4019  df-op 4023  df-uni 4236  df-br 4440  df-opab 4498  df-mpt 4499  df-id 4784  df-xp 4994  df-rel 4995  df-cnv 4996  df-co 4997  df-dm 4998  df-rn 4999  df-res 5000  df-ima 5001  df-fun 5572  df-fn 5573  df-f 5574  df-f1 5575  df-fo 5576  df-f1o 5577  df-er 7303  df-en 7510  df-dom 7511  df-sdom 7512  df-wdom 7977
This theorem is referenced by:  hsmexlem4  8800
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