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 Description: Virtual deduction proof of the left-to-right implication of dftr4 4309. A transitive class is a subset of its power class. This proof corresponds to the virtual deduction proof of dftr4 4309 without accumulating results. (Contributed by Alan Sare, 29-Apr-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression

Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfss2 3339 . . 3
2 idn1 28727 . . . . . . 7
3 idn2 28776 . . . . . . 7
4 trss 4313 . . . . . . 7
52, 3, 4e12 28898 . . . . . 6
6 vex 2961 . . . . . . 7
76elpw 3807 . . . . . 6
85, 7e2bir 28796 . . . . 5
98in2 28768 . . . 4
109gen11 28779 . . 3
11 bi2 191 . . 3
121, 10, 11e01 28854 . 2
1312in1 28724 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178  wal 1550   wcel 1726   wss 3322  cpw 3801   wtr 4304 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-v 2960  df-in 3329  df-ss 3336  df-pw 3803  df-uni 4018  df-tr 4305  df-vd1 28723  df-vd2 28732
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