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Theorem 3oalem4 31185
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 4227 . 2 ((⊥‘𝐵) ∩ (𝐵 𝐴)) ⊆ (⊥‘𝐵)
31, 2eqsstri 4015 1 𝑅 ⊆ (⊥‘𝐵)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1539  cin 3946  wss 3947  cfv 6542  (class class class)co 7411  cort 30450   chj 30453
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1911  ax-6 1969  ax-7 2009  ax-8 2106  ax-9 2114  ax-ext 2701
This theorem depends on definitions:  df-bi 206  df-an 395  df-tru 1542  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2722  df-clel 2808  df-v 3474  df-in 3954  df-ss 3964
This theorem is referenced by:  3oalem5  31186
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