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Theorem csbabgOLD 37211
 Description: Move substitution into a class abstraction. (Contributed by NM, 13-Dec-2005.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) Obsolete as of 19-Aug-2018. Use csbab 3797 instead. (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
csbabgOLD
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   ()   (,)

Proof of Theorem csbabgOLD
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbccom 3339 . . . 4
2 df-clab 2438 . . . . 5
3 sbsbc 3271 . . . . 5
42, 3bitri 253 . . . 4
5 df-clab 2438 . . . . . 6
6 sbsbc 3271 . . . . . 6
75, 6bitri 253 . . . . 5
87sbcbii 3323 . . . 4
91, 4, 83bitr4i 281 . . 3
10 sbcel2gOLD 36906 . . 3
119, 10syl5rbb 262 . 2
1211eqrdv 2449 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1444  wsb 1797   wcel 1887  cab 2437  wsbc 3267  csb 3363 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-v 3047  df-sbc 3268  df-csb 3364 This theorem is referenced by:  csbunigOLD  37212  csbfv12gALTOLD  37213  csbxpgOLD  37214  csbrngOLD  37217  csbingVD  37281  csbsngVD  37290  csbxpgVD  37291  csbrngVD  37293  csbunigVD  37295  csbfv12gALTVD  37296
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