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Theorem iineq2i 3880
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 3878 . 2 (∀𝑥𝐴 𝐵 = 𝐶 𝑥𝐴 𝐵 = 𝑥𝐴 𝐶)
2 iuneq2i.1 . 2 (𝑥𝐴𝐵 = 𝐶)
31, 2mprg 2521 1 𝑥𝐴 𝐵 = 𝑥𝐴 𝐶
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1342  wcel 2135   ciin 3862
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1434  ax-7 1435  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-8 1491  ax-11 1493  ax-4 1497  ax-17 1513  ax-i9 1517  ax-ial 1521  ax-i5r 1522  ax-ext 2146
This theorem depends on definitions:  df-bi 116  df-tru 1345  df-nf 1448  df-sb 1750  df-clab 2151  df-cleq 2157  df-clel 2160  df-ral 2447  df-iin 3864
This theorem is referenced by:  iinrabm  3923  iinin1m  3930
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