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Theorem cbvcsb 3140
 Description: Change bound variables in a class substitution. Interestingly, this does not require any bound variable conditions on . (Contributed by Jeff Hankins, 13-Sep-2009.) (Revised by Mario Carneiro, 11-Dec-2016.)
Hypotheses
Ref Expression
cbvcsb.1
cbvcsb.2
cbvcsb.3
Assertion
Ref Expression
cbvcsb

Proof of Theorem cbvcsb
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 cbvcsb.1 . . . . 5
21nfcri 2483 . . . 4
3 cbvcsb.2 . . . . 5
43nfcri 2483 . . . 4
5 cbvcsb.3 . . . . 5
65eleq2d 2420 . . . 4
72, 4, 6cbvsbc 3074 . . 3
87abbii 2465 . 2
9 df-csb 3137 . 2
10 df-csb 3137 . 2
118, 9, 103eqtr4i 2383 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1642   wcel 1710  cab 2339  wnfc 2476  wsbc 3046  csb 3136 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-sbc 3047  df-csb 3137 This theorem is referenced by:  cbvcsbv  3141
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