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Theorem cbviinv 4526
Description: Change bound variables in an indexed intersection. (Contributed by Jeff Hankins, 26-Aug-2009.)
Hypothesis
Ref Expression
cbviunv.1 (𝑥 = 𝑦𝐵 = 𝐶)
Assertion
Ref Expression
cbviinv 𝑥𝐴 𝐵 = 𝑦𝐴 𝐶
Distinct variable groups:   𝑥,𝐴   𝑦,𝐴   𝑦,𝐵   𝑥,𝐶
Allowed substitution hints:   𝐵(𝑥)   𝐶(𝑦)

Proof of Theorem cbviinv
StepHypRef Expression
1 nfcv 2761 . 2 𝑦𝐵
2 nfcv 2761 . 2 𝑥𝐶
3 cbviunv.1 . 2 (𝑥 = 𝑦𝐵 = 𝐶)
41, 2, 3cbviin 4524 1 𝑥𝐴 𝐵 = 𝑦𝐴 𝐶
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1480   ciin 4486
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-ral 2912  df-iin 4488
This theorem is referenced by:  meaiininc  40005  iinhoiicc  40192  smflimlem3  40285  smflimlem4  40286  smflimlem6  40288  smfsuplem2  40322  smflimsuplem1  40330  smflimsup  40338
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