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Theorem dmiin 4753
 Description: Domain of an intersection. (Contributed by FL, 15-Oct-2012.)
Assertion
Ref Expression
dmiin

Proof of Theorem dmiin
StepHypRef Expression
1 nfii1 3812 . . . 4
21nfdm 4751 . . 3
32ssiinf 3830 . 2
4 iinss2 3833 . . 3
5 dmss 4706 . . 3
64, 5syl 14 . 2
73, 6mprgbir 2465 1
 Colors of variables: wff set class Syntax hints:   wcel 1463   wss 3039  ciin 3782   cdm 4507 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-3an 947  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-ral 2396  df-v 2660  df-un 3043  df-in 3045  df-ss 3052  df-sn 3501  df-pr 3502  df-op 3504  df-iin 3784  df-br 3898  df-dm 4517 This theorem is referenced by: (None)
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