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Theorem cnvimass 4718
 Description: A preimage under any class is included in the domain of the class. (Contributed by FL, 29-Jan-2007.)
Assertion
Ref Expression
cnvimass (𝐴𝐵) ⊆ dom 𝐴

Proof of Theorem cnvimass
StepHypRef Expression
1 imassrn 4709 . 2 (𝐴𝐵) ⊆ ran 𝐴
2 dfdm4 4555 . 2 dom 𝐴 = ran 𝐴
31, 2sseqtr4i 3033 1 (𝐴𝐵) ⊆ dom 𝐴
 Colors of variables: wff set class Syntax hints:   ⊆ wss 2974  ◡ccnv 4370  dom cdm 4371  ran crn 4372   “ cima 4374 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3904  ax-pow 3956  ax-pr 3972 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-eu 1945  df-mo 1946  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-rex 2355  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-pw 3392  df-sn 3412  df-pr 3413  df-op 3415  df-br 3794  df-opab 3848  df-xp 4377  df-cnv 4379  df-dm 4381  df-rn 4382  df-res 4383  df-ima 4384 This theorem is referenced by:  fvimacnvi  5313  elpreima  5318  fconst4m  5413  nn0supp  8407
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