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Theorem sspwtrALT 37273
 Description: Virtual deduction proof of sspwtr 37272. This proof is the same as the proof of sspwtr 37272 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 4492 . . 3
2 simpr 468 . . . . . 6
3 ssel 3412 . . . . . 6
4 elpwi 3951 . . . . . 6
52, 3, 4syl56 34 . . . . 5
6 idd 24 . . . . . 6
7 simpl 464 . . . . . 6
86, 7syl6 33 . . . . 5
9 ssel 3412 . . . . 5
105, 8, 9syl6c 65 . . . 4
1110alrimivv 1782 . . 3
12 biimpr 203 . . 3
131, 11, 12mpsyl 64 . 2
1413idiALT 36902 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wa 376  wal 1450   wcel 1904   wss 3390  cpw 3942   wtr 4490 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-v 3033  df-in 3397  df-ss 3404  df-pw 3944  df-uni 4191  df-tr 4491 This theorem is referenced by: (None)
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