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Theorem pwtrrVD 28875
 Description: Virtual deduction proof of pwtr 4408. (Contributed by Alan Sare, 25-Aug-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
pwtrrVD.1
Assertion
Ref Expression
pwtrrVD

Proof of Theorem pwtrrVD
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 dftr2 4296 . . 3
2 idn1 28602 . . . . . . . 8
3 idn2 28651 . . . . . . . . 9
4 simpr 448 . . . . . . . . 9
53, 4e2 28669 . . . . . . . 8
6 pwtrrVD.1 . . . . . . . . 9
76pwid 3804 . . . . . . . 8
8 trel 4301 . . . . . . . . 9
98exp3a 426 . . . . . . . 8
102, 5, 7, 9e120 28701 . . . . . . 7
11 elpwi 3799 . . . . . . 7
1210, 11e2 28669 . . . . . 6
13 simpl 444 . . . . . . 7
143, 13e2 28669 . . . . . 6
15 ssel 3334 . . . . . 6
1612, 14, 15e22 28709 . . . . 5
1716in2 28643 . . . 4
1817gen12 28656 . . 3
19 bi2 190 . . 3
201, 18, 19e01 28729 . 2
2120in1 28599 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549   wcel 1725  cvv 2948   wss 3312  cpw 3791   wtr 4294 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 2416 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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-in 3319  df-ss 3326  df-pw 3793  df-uni 4008  df-tr 4295  df-vd1 28598  df-vd2 28607
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