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Theorem trsspwALT 37269
 Description: Virtual deduction proof of the left-to-right implication of dftr4 4495. A transitive class is a subset of its power class. This proof corresponds to the virtual deduction proof of dftr4 4495 without accumulating results. (Contributed by Alan Sare, 29-Apr-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
trsspwALT

Proof of Theorem trsspwALT
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfss2 3407 . . 3
2 idn1 37012 . . . . . . 7
3 idn2 37060 . . . . . . 7
4 trss 4499 . . . . . . 7
52, 3, 4e12 37174 . . . . . 6
6 vex 3034 . . . . . . 7
76elpw 3948 . . . . . 6
85, 7e2bir 37080 . . . . 5
98in2 37052 . . . 4
109gen11 37063 . . 3
11 biimpr 203 . . 3
121, 10, 11e01 37138 . 2
1312in1 37009 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189  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-ral 2761  df-v 3033  df-in 3397  df-ss 3404  df-pw 3944  df-uni 4191  df-tr 4491  df-vd1 37008  df-vd2 37016 This theorem is referenced by: (None)
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