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Theorem cbviunv 3687
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 2175 . 2 yB
2 nfcv 2175 . 2 x𝐶
3 cbviunv.1 . 2 (x = yB = 𝐶)
41, 2, 3cbviun 3685 1 x A B = y A 𝐶
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242   ciun 3648
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-iun 3650
This theorem is referenced by:  iunxdif2  3696
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