 New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  vdif0 GIF version

Theorem vdif0 3610
 Description: Universal class equality in terms of empty difference. (Contributed by NM, 17-Sep-2003.)
Assertion
Ref Expression
vdif0 (A = V ↔ (V A) = )

Proof of Theorem vdif0
StepHypRef Expression
1 vss 3587 . 2 (V AA = V)
2 ssdif0 3609 . 2 (V A ↔ (V A) = )
31, 2bitr3i 242 1 (A = V ↔ (V A) = )
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   = wceq 1642  Vcvv 2859   ∖ cdif 3206   ⊆ wss 3257  ∅c0 3550 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215  df-ss 3259  df-nul 3551 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator