Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  opeq1i Unicode version

Theorem opeq1i 3744
 Description: Equality inference for ordered pairs. (Contributed by NM, 16-Dec-2006.)
Hypothesis
Ref Expression
opeq1i.1
Assertion
Ref Expression
opeq1i

Proof of Theorem opeq1i
StepHypRef Expression
1 opeq1i.1 . 2
2 opeq1 3741 . 2
31, 2ax-mp 5 1
 Colors of variables: wff set class Syntax hints:   wceq 1335  cop 3563 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-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-un 3106  df-sn 3566  df-pr 3567  df-op 3569 This theorem is referenced by:  caucvgsrlemfv  7694  caucvgsr  7705  pitonnlem1  7748  axi2m1  7778  axcaucvg  7803  ennnfonelem1  12108  2strstr1g  12253  2strop1g  12255
 Copyright terms: Public domain W3C validator