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Theorem csbvarg 3163
 Description: The proper substitution of a class for setvar variable results in the class (if the class exists). (Contributed by NM, 10-Nov-2005.)
Assertion
Ref Expression
csbvarg

Proof of Theorem csbvarg
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 elex 2867 . 2
2 vex 2862 . . . . . 6
3 df-csb 3137 . . . . . . 7
4 sbcel2gv 3106 . . . . . . . 8
54abbi1dv 2469 . . . . . . 7
63, 5syl5eq 2397 . . . . . 6
72, 6ax-mp 8 . . . . 5
87csbeq2i 3162 . . . 4
9 csbco 3145 . . . 4
10 df-csb 3137 . . . 4
118, 9, 103eqtr3i 2381 . . 3
12 sbcel2gv 3106 . . . 4
1312abbi1dv 2469 . . 3
1411, 13syl5eq 2397 . 2
151, 14syl 15 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1642   wcel 1710  cab 2339  cvv 2859  wsbc 3046  csb 3136 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-sbc 3047  df-csb 3137 This theorem is referenced by:  sbccsb2g  3165  csbfvg  5338
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