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Theorem cbviinv 3958
Description: Change bound variables in an indexed intersection. (Contributed by Jeff Hankins, 26-Aug-2009.)
Hypothesis
Ref Expression
cbviunv.1  |-  ( x  =  y  ->  B  =  C )
Assertion
Ref Expression
cbviinv  |-  |^|_ x  e.  A  B  =  |^|_ y  e.  A  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 2432 . 2  |-  F/_ y B
2 nfcv 2432 . 2  |-  F/_ x C
3 cbviunv.1 . 2  |-  ( x  =  y  ->  B  =  C )
41, 2, 3cbviin 3956 1  |-  |^|_ x  e.  A  B  =  |^|_ y  e.  A  C
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1632   |^|_ciin 3922
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-iin 3924
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