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 Description: Virtual deduction proof of the left-to-right implication of dftr4 4015. A transitive class is a subset of its power class. This proof corresponds to the virtual deduction proof of dftr4 4015 without accumulating results. (Contributed by Alan Sare, 29-Apr-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression

StepHypRef Expression
1 dfss2 3092 . . 3
2 idn1 27035 . . . . . . 7
3 idn2 27075 . . . . . . 7
4 trss 4019 . . . . . . 7
52, 3, 4e12 27189 . . . . . 6
6 vex 2730 . . . . . . 7
76elpw 3536 . . . . . 6
85, 7e2bir 27095 . . . . 5
98in2 27067 . . . 4
109gen11 27078 . . 3
11 bi2 191 . . 3
121, 10, 11e01 27153 . 2
1312in1 27032 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178  wal 1532   wcel 1621   wss 3078  cpw 3530   wtr 4010 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ral 2513  df-v 2729  df-in 3085  df-ss 3089  df-pw 3532  df-uni 3728  df-tr 4011  df-vd1 27031  df-vd2 27040
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