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Theorem dmiin 4938
 Description: Domain of an intersection. (Contributed by FL, 15-Oct-2012.)
Assertion
Ref Expression
dmiin

Proof of Theorem dmiin
StepHypRef Expression
1 nfii1 3950 . . . 4
21nfdm 4936 . . 3
32ssiinf 3967 . 2
4 iinss2 3970 . . 3
5 dmss 4894 . . 3
64, 5syl 15 . 2
73, 6mprgbir 2626 1
 Colors of variables: wff set class Syntax hints:   wcel 1696   wss 3165  ciin 3922   cdm 4705 This theorem is referenced by:  domintrefc  25228  rnintintrn  25229 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-iin 3924  df-br 4040  df-dm 4715
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