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

Theorem inteqi 3930
 Description: Equality inference for class intersection. (Contributed by NM, 2-Sep-2003.)
Hypothesis
Ref Expression
inteqi.1 A = B
Assertion
Ref Expression
inteqi A = B

Proof of Theorem inteqi
StepHypRef Expression
1 inteqi.1 . 2 A = B
2 inteq 3929 . 2 (A = BA = B)
31, 2ax-mp 8 1 A = B
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642  ∩cint 3926 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-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-int 3927 This theorem is referenced by:  elintrab  3938  ssintrab  3949  intmin2  3953  intsng  3961  dfnnc2  4395  spfinex  4537  dfnnc3  5885
 Copyright terms: Public domain W3C validator