New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  iuneq2i GIF version

Theorem iuneq2i 3987
 Description: Equality inference for indexed union. (Contributed by NM, 22-Oct-2003.)
Hypothesis
Ref Expression
iuneq2i.1 (x AB = C)
Assertion
Ref Expression
iuneq2i x A B = x A C

Proof of Theorem iuneq2i
StepHypRef Expression
1 iuneq2 3985 . 2 (x A B = Cx A B = x A C)
2 iuneq2i.1 . 2 (x AB = C)
31, 2mprg 2683 1 x A B = x A C
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642   ∈ wcel 1710  ∪ciun 3969 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rex 2620  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-iun 3971 This theorem is referenced by:  iunrab  4013  iunid  4021  iunin1  4031  2iunin  4034  dfimafn2  5367  funiunfv  5467  uniqs  5984
 Copyright terms: Public domain W3C validator