Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  dfint2 Structured version   Visualization version   Unicode version

Theorem dfint2 4228
 Description: Alternate definition of class intersection. (Contributed by NM, 28-Jun-1998.)
Assertion
Ref Expression
dfint2
Distinct variable group:   ,,

Proof of Theorem dfint2
StepHypRef Expression
1 df-int 4227 . 2
2 df-ral 2761 . . 3
32abbii 2587 . 2
41, 3eqtr4i 2496 1
 Colors of variables: wff setvar class Syntax hints:   wi 4  wal 1450   wceq 1452   wcel 1904  cab 2457  wral 2756  cint 4226 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-ral 2761  df-int 4227 This theorem is referenced by:  inteq  4229  nfint  4236  intss  4247  intiin  4323  dfint3  30790
 Copyright terms: Public domain W3C validator