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Theorem sbcssOLD 28564
 Description: Distribute proper substitution through a subclass relation. This theorem was automatically derived from sbcssVD 28932. (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 3329 . . . 4
21sbcbiiOLD 3209 . . 3
3 sbcalg 3201 . . . 4
4 sbcimg 3194 . . . . . . 7
5 sbcel2g 3264 . . . . . . . 8
6 sbcel2g 3264 . . . . . . . 8
75, 6imbi12d 312 . . . . . . 7
84, 7bitrd 245 . . . . . 6
98alrimiv 1641 . . . . 5
10 albi 1573 . . . . 5
119, 10syl 16 . . . 4
123, 11bitrd 245 . . 3
132, 12bitrd 245 . 2
14 dfss2 3329 . 2
1513, 14syl6bbr 255 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wal 1549   wcel 1725  wsbc 3153  csb 3243   wss 3312 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-sbc 3154  df-csb 3244  df-in 3319  df-ss 3326
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