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Theorem 3oalem4 31693
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 4244 . 2 ((⊥‘𝐵) ∩ (𝐵 𝐴)) ⊆ (⊥‘𝐵)
31, 2eqsstri 4029 1 𝑅 ⊆ (⊥‘𝐵)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1536  cin 3961  wss 3962  cfv 6562  (class class class)co 7430  cort 30958   chj 30961
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-ext 2705
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1539  df-ex 1776  df-sb 2062  df-clab 2712  df-cleq 2726  df-clel 2813  df-v 3479  df-in 3969  df-ss 3979
This theorem is referenced by:  3oalem5  31694
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