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Theorem f1dom 8848
Description: The domain of a one-to-one function is dominated by its codomain. (Contributed by NM, 19-Jun-1998.)
Hypothesis
Ref Expression
f1dom.1 𝐵 ∈ V
Assertion
Ref Expression
f1dom (𝐹:𝐴1-1𝐵𝐴𝐵)

Proof of Theorem f1dom
StepHypRef Expression
1 f1dom.1 . 2 𝐵 ∈ V
2 f1domg 8846 . 2 (𝐵 ∈ V → (𝐹:𝐴1-1𝐵𝐴𝐵))
31, 2ax-mp 5 1 (𝐹:𝐴1-1𝐵𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wcel 2107  Vcvv 3444   class class class wbr 5104  1-1wf1 6489  cdom 8815
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2709  ax-rep 5241  ax-sep 5255  ax-nul 5262  ax-pr 5383  ax-un 7663
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-nf 1787  df-sb 2069  df-mo 2540  df-eu 2569  df-clab 2716  df-cleq 2730  df-clel 2816  df-nfc 2888  df-ne 2943  df-ral 3064  df-rex 3073  df-reu 3353  df-rab 3407  df-v 3446  df-sbc 3739  df-csb 3855  df-dif 3912  df-un 3914  df-in 3916  df-ss 3926  df-nul 4282  df-if 4486  df-sn 4586  df-pr 4588  df-op 4592  df-uni 4865  df-iun 4955  df-br 5105  df-opab 5167  df-mpt 5188  df-id 5529  df-xp 5637  df-rel 5638  df-cnv 5639  df-co 5640  df-dm 5641  df-rn 5642  df-res 5643  df-ima 5644  df-iota 6444  df-fun 6494  df-fn 6495  df-f 6496  df-f1 6497  df-fo 6498  df-f1o 6499  df-fv 6500  df-dom 8819
This theorem is referenced by:  dominf  10315  dominfac  10443  lgsqrlem4  26625
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