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Theorem inv1 3430
 Description: The intersection of a class with the universal class is itself. Exercise 4.10(k) of [Mendelson] p. 231. (Contributed by NM, 17-May-1998.)
Assertion
Ref Expression
inv1

Proof of Theorem inv1
StepHypRef Expression
1 inss1 3327 . 2
2 ssid 3148 . . 3
3 ssv 3150 . . 3
42, 3ssini 3330 . 2
51, 4eqssi 3144 1
 Colors of variables: wff set class Syntax hints:   wceq 1335  cvv 2712   cin 3101 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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-in 3108  df-ss 3115 This theorem is referenced by:  rint0  3846  riin0  3920  xpssres  4900  resdmdfsn  4908  imainrect  5030  xpima2m  5032  dmresv  5043
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