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

Theorem difrab 3529
 Description: Difference of two restricted class abstractions. (Contributed by NM, 23-Oct-2004.)
Assertion
Ref Expression
difrab

Proof of Theorem difrab
StepHypRef Expression
1 df-rab 2623 . . 3
2 df-rab 2623 . . 3
31, 2difeq12i 3383 . 2
4 df-rab 2623 . . 3
5 difab 3523 . . . 4
6 anass 630 . . . . . 6
7 simpr 447 . . . . . . . . 9
87con3i 127 . . . . . . . 8
98anim2i 552 . . . . . . 7
10 pm3.2 434 . . . . . . . . . 10
1110adantr 451 . . . . . . . . 9
1211con3d 125 . . . . . . . 8
1312imdistani 671 . . . . . . 7
149, 13impbii 180 . . . . . 6
156, 14bitr3i 242 . . . . 5
1615abbii 2465 . . . 4
175, 16eqtr4i 2376 . . 3
184, 17eqtr4i 2376 . 2
193, 18eqtr4i 2376 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 358   wceq 1642   wcel 1710  cab 2339  crab 2618   cdif 3206 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-rab 2623  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator