Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  dfnul3 Structured version   Unicode version

Theorem dfnul3 3633
 Description: Alternate definition of the empty set. (Contributed by NM, 25-Mar-2004.)
Assertion
Ref Expression
dfnul3

Proof of Theorem dfnul3
StepHypRef Expression
1 pm3.24 854 . . . . 5
2 equid 1689 . . . . 5
31, 22th 232 . . . 4
43con1bii 323 . . 3
54abbii 2550 . 2
6 dfnul2 3632 . 2
7 df-rab 2716 . 2
85, 6, 73eqtr4i 2468 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 360   wceq 1653   wcel 1726  cab 2424  crab 2711  c0 3630 This theorem is referenced by:  difidALT  3699  kmlem3  8037 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rab 2716  df-v 2960  df-dif 3325  df-nul 3631
 Copyright terms: Public domain W3C validator