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Theorem sspwtrALT 28935
 Description: Virtual deduction proof of sspwtr 28934. This proof is the same as the proof of sspwtr 28934 except each virtual deduction symbol is replaced by its non-virtual deduction symbol equivalent. A class which is a subclass of its power class is transitive. (Contributed by Alan Sare, 3-May-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
sspwtrALT

Proof of Theorem sspwtrALT
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 dftr2 4304 . . 3
2 simpr 448 . . . . . . 7
3 ssel 3342 . . . . . . 7
4 elpwi 3807 . . . . . . 7
52, 3, 4syl56 32 . . . . . 6
6 idd 22 . . . . . . 7
7 simpl 444 . . . . . . 7
86, 7syl6 31 . . . . . 6
9 ssel 3342 . . . . . 6
105, 8, 9ee22 1371 . . . . 5
1110idi 2 . . . 4
1211alrimivv 1642 . . 3
13 bi2 190 . . 3
141, 12, 13mpsyl 61 . 2
1514idi 2 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549   wcel 1725   wss 3320  cpw 3799   wtr 4302 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 2417 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 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-in 3327  df-ss 3334  df-pw 3801  df-uni 4016  df-tr 4303
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