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

Theorem 3oalem4 28652
Description: Lemma for 3OA (weak) orthoarguesian law. (Contributed by NM, 19-Oct-1999.) (New usage is discouraged.)
Hypothesis
Ref Expression
3oalem4.3 𝑅 = ((⊥‘𝐵) ∩ (𝐵 𝐴))
Assertion
Ref Expression
3oalem4 𝑅 ⊆ (⊥‘𝐵)

Proof of Theorem 3oalem4
StepHypRef Expression
1 3oalem4.3 . 2 𝑅 = ((⊥‘𝐵) ∩ (𝐵 𝐴))
2 inss1 3866 . 2 ((⊥‘𝐵) ∩ (𝐵 𝐴)) ⊆ (⊥‘𝐵)
31, 2eqsstri 3668 1 𝑅 ⊆ (⊥‘𝐵)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1523  cin 3606  wss 3607  cfv 5926  (class class class)co 6690  cort 27915   chj 27918
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-v 3233  df-in 3614  df-ss 3621
This theorem is referenced by:  3oalem5  28653
  Copyright terms: Public domain W3C validator