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Theorem sbcssOLD 36878
 Description: Distribute proper substitution through a subclass relation. This theorem was automatically derived from sbcssgVD 37254. (Contributed by Alan Sare, 22-Jul-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
sbcssOLD

Proof of Theorem sbcssOLD
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfss2 3453 . . . 4
21sbcbiiOLD 36863 . . 3
3 sbcalgOLD 36874 . . . 4
4 sbcimg 3341 . . . . . . 7
5 sbcel2gOLD 36877 . . . . . . . 8
6 sbcel2gOLD 36877 . . . . . . . 8
75, 6imbi12d 321 . . . . . . 7
84, 7bitrd 256 . . . . . 6
98alrimiv 1767 . . . . 5
10 albi 1684 . . . . 5
119, 10syl 17 . . . 4
123, 11bitrd 256 . . 3
132, 12bitrd 256 . 2
14 dfss2 3453 . 2
1513, 14syl6bbr 266 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187  wal 1435   wcel 1872  wsbc 3299  csb 3395   wss 3436 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-v 3082  df-sbc 3300  df-csb 3396  df-in 3443  df-ss 3450 This theorem is referenced by: (None)
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