HSE Home Hilbert Space Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  HSE Home  >  Th. List  >  3oalem4 Structured version   Unicode version

Theorem 3oalem4 26710
Description: Lemma for 3OA (weak) orthoarguesian law. (Contributed by NM, 19-Oct-1999.) (New usage is discouraged.)
Hypothesis
Ref Expression
3oalem4.3  |-  R  =  ( ( _|_ `  B
)  i^i  ( B  vH  A ) )
Assertion
Ref Expression
3oalem4  |-  R  C_  ( _|_ `  B )

Proof of Theorem 3oalem4
StepHypRef Expression
1 3oalem4.3 . 2  |-  R  =  ( ( _|_ `  B
)  i^i  ( B  vH  A ) )
2 inss1 3714 . 2  |-  ( ( _|_ `  B )  i^i  ( B  vH  A ) )  C_  ( _|_ `  B )
31, 2eqsstri 3529 1  |-  R  C_  ( _|_ `  B )
Colors of variables: wff setvar class
Syntax hints:    = wceq 1395    i^i cin 3470    C_ wss 3471   ` cfv 5594  (class class class)co 6296   _|_cort 25974    vH chj 25977
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-in 3478  df-ss 3485
This theorem is referenced by:  3oalem5  26711
  Copyright terms: Public domain W3C validator