Mathbox for Alan Sare < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  sspwtr Structured version   Unicode version

Theorem sspwtr 28835
 Description: Virtual deduction proof of the right-to-left implication of dftr4 4299. A class which is a subclass of its power class is transitive. This proof corresponds to the virtual deduction proof of sspwtr 28835 without accumulating results. (Contributed by Alan Sare, 2-May-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
sspwtr

Proof of Theorem sspwtr
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 dftr2 4296 . . 3
2 idn1 28566 . . . . . . . 8
3 idn2 28615 . . . . . . . . 9
4 simpr 448 . . . . . . . . 9
53, 4e2 28633 . . . . . . . 8
6 ssel 3334 . . . . . . . 8
72, 5, 6e12 28737 . . . . . . 7
8 elpwi 3799 . . . . . . 7
97, 8e2 28633 . . . . . 6
10 simpl 444 . . . . . . 7
113, 10e2 28633 . . . . . 6
12 ssel 3334 . . . . . 6
139, 11, 12e22 28673 . . . . 5
1413in2 28607 . . . 4
1514gen12 28620 . . 3
16 bi2 190 . . 3
171, 15, 16e01 28693 . 2
1817in1 28563 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549   wcel 1725   wss 3312  cpw 3791   wtr 4294 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-in 3319  df-ss 3326  df-pw 3793  df-uni 4008  df-tr 4295  df-vd1 28562  df-vd2 28571
 Copyright terms: Public domain W3C validator