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Theorem cbviunv 4005
 Description: Rule used to change the bound variables in an indexed union, with the substitution specified implicitly by the hypothesis. (Contributed by NM, 15-Sep-2003.)
Hypothesis
Ref Expression
cbviunv.1 (x = yB = C)
Assertion
Ref Expression
cbviunv x A B = y A C
Distinct variable groups:   x,A   y,A   y,B   x,C
Allowed substitution hints:   B(x)   C(y)

Proof of Theorem cbviunv
StepHypRef Expression
1 nfcv 2489 . 2 yB
2 nfcv 2489 . 2 xC
3 cbviunv.1 . 2 (x = yB = C)
41, 2, 3cbviun 4003 1 x A B = y A C
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642  ∪ciun 3969 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-ral 2619  df-rex 2620  df-iun 3971 This theorem is referenced by:  iunxdif2  4014
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