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Theorem iineq2i 3940
Description: Equality inference for indexed intersection. (Contributed by NM, 22-Oct-2003.)
Hypothesis
Ref Expression
iuneq2i.1  |-  ( x  e.  A  ->  B  =  C )
Assertion
Ref Expression
iineq2i  |-  |^|_ x  e.  A  B  =  |^|_
x  e.  A  C

Proof of Theorem iineq2i
StepHypRef Expression
1 iineq2 3938 . 2  |-  ( A. x  e.  A  B  =  C  ->  |^|_ x  e.  A  B  =  |^|_
x  e.  A  C
)
2 iuneq2i.1 . 2  |-  ( x  e.  A  ->  B  =  C )
31, 2mprg 2625 1  |-  |^|_ x  e.  A  B  =  |^|_
x  e.  A  C
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1632    e. wcel 1696   |^|_ciin 3922
This theorem is referenced by:  iinrab  3980  iinin1  3989  rnintintrn  25229  imaiinfv  26862  diaintclN  31870  dibintclN  31979  dihintcl  32156
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-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-ral 2561  df-iin 3924
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