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Theorem iineq2i 4104
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 4102 . 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 2767 1  |-  |^|_ x  e.  A  B  =  |^|_
x  e.  A  C
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1652    e. wcel 1725   |^|_ciin 4086
This theorem is referenced by:  iinrab  4145  iinin1  4154  imaiinfv  26694  diaintclN  31757  dibintclN  31866  dihintcl  32043
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-ral 2702  df-iin 4088
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