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Theorem wdomimag 7914
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 5604 . 2  |-  ( ( Fun  F  /\  A  e.  V )  ->  ( F " A )  e. 
_V )
2 wdomima2g 7913 . 2  |-  ( ( Fun  F  /\  A  e.  V  /\  ( F " A )  e. 
_V )  ->  ( F " A )  ~<_*  A
)
31, 2mpd3an3 1316 1  |-  ( ( Fun  F  /\  A  e.  V )  ->  ( F " A )  ~<_*  A
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369    e. wcel 1758   _Vcvv 3078   class class class wbr 4401   "cima 4952   Fun wfun 5521    ~<_* cwdom 7884
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 4512  ax-sep 4522  ax-nul 4530  ax-pow 4579  ax-pr 4640  ax-un 6483
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 2804  df-rex 2805  df-rab 2808  df-v 3080  df-dif 3440  df-un 3442  df-in 3444  df-ss 3451  df-nul 3747  df-if 3901  df-pw 3971  df-sn 3987  df-pr 3989  df-op 3993  df-uni 4201  df-br 4402  df-opab 4460  df-mpt 4461  df-id 4745  df-xp 4955  df-rel 4956  df-cnv 4957  df-co 4958  df-dm 4959  df-rn 4960  df-res 4961  df-ima 4962  df-fun 5529  df-fn 5530  df-f 5531  df-f1 5532  df-fo 5533  df-f1o 5534  df-er 7212  df-en 7422  df-dom 7423  df-sdom 7424  df-wdom 7886
This theorem is referenced by:  hsmexlem4  8710
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