ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  iineq2i GIF version

Theorem iineq2i 3917
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 3915 . 2 (∀𝑥𝐴 𝐵 = 𝐶 𝑥𝐴 𝐵 = 𝑥𝐴 𝐶)
2 iuneq2i.1 . 2 (𝑥𝐴𝐵 = 𝐶)
31, 2mprg 2544 1 𝑥𝐴 𝐵 = 𝑥𝐴 𝐶
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1363  wcel 2158   ciin 3899
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-11 1516  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169
This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-ral 2470  df-iin 3901
This theorem is referenced by:  iinrabm  3961  iinin1m  3968
  Copyright terms: Public domain W3C validator