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Theorem suctrALT2 28850
 Description: Virtual deduction proof of suctr 4657. The sucessor of a transitive class is transitive. This proof was generated automatically from the virtual deduction proof suctrALT2VD 28849 using the tools command file translatewithout_overwritingminimize_excludingduplicates.cmd . (Contributed by Alan Sare, 11-Sep-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
suctrALT2

Proof of Theorem suctrALT2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 sssucid 4650 . . . . 5
2 trel 4301 . . . . . . 7
32exp3a 426 . . . . . 6
43adantrd 455 . . . . 5
5 ssel 3334 . . . . 5
61, 4, 5ee03 28754 . . . 4
7 simpl 444 . . . . . . 7
87a1i 11 . . . . . 6
9 eleq2 2496 . . . . . . 7
109biimpcd 216 . . . . . 6
118, 10syl6 31 . . . . 5
121, 11, 5ee03 28754 . . . 4
13 simpr 448 . . . . . 6
1413a1i 11 . . . . 5
15 elsuci 4639 . . . . 5
1614, 15syl6 31 . . . 4
17 jao 499 . . . 4
186, 12, 16, 17ee222 28485 . . 3
1918alrimivv 1642 . 2
20 dftr2 4296 . 2
2119, 20sylibr 204 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 358   wa 359  wal 1549   wceq 1652   wcel 1725   wss 3312   wtr 4294   csuc 4575 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-un 3317  df-in 3319  df-ss 3326  df-sn 3812  df-uni 4008  df-tr 4295  df-suc 4579
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