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Theorem iineq2i 3726
Description: Equality inference for indexed intersection. (Contributed by NM, 22-Oct-2003.)
Hypothesis
Ref Expression
iuneq2i.1 (𝑥𝐴𝐵 = 𝐶)
Assertion
Ref Expression
iineq2i 𝑥𝐴 𝐵 = 𝑥𝐴 𝐶

Proof of Theorem iineq2i
StepHypRef Expression
1 iineq2 3724 . 2 (∀𝑥𝐴 𝐵 = 𝐶 𝑥𝐴 𝐵 = 𝑥𝐴 𝐶)
2 iuneq2i.1 . 2 (𝑥𝐴𝐵 = 𝐶)
31, 2mprg 2428 1 𝑥𝐴 𝐵 = 𝑥𝐴 𝐶
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1287  wcel 1436   ciin 3708
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-11 1440  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-ral 2360  df-iin 3710
This theorem is referenced by:  iinrabm  3769  iinin1m  3776
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