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Theorem cbvcsbv 3141
 Description: Change the bound variable of a proper substitution into a class using implicit substitution. (Contributed by NM, 30-Sep-2008.) (Revised by Mario Carneiro, 13-Oct-2016.)
Hypothesis
Ref Expression
cbvcsbv.1 (x = yB = C)
Assertion
Ref Expression
cbvcsbv [A / x]B = [A / y]C
Distinct variable groups:   x,y   y,B   x,C
Allowed substitution hints:   A(x,y)   B(x)   C(y)

Proof of Theorem cbvcsbv
StepHypRef Expression
1 nfcv 2489 . 2 yB
2 nfcv 2489 . 2 xC
3 cbvcsbv.1 . 2 (x = yB = C)
41, 2, 3cbvcsb 3140 1 [A / x]B = [A / y]C
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642  [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: (None)
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