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Theorem 3oalem4 31684
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 4237 . 2 ((⊥‘𝐵) ∩ (𝐵 𝐴)) ⊆ (⊥‘𝐵)
31, 2eqsstri 4030 1 𝑅 ⊆ (⊥‘𝐵)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  cin 3950  wss 3951  cfv 6561  (class class class)co 7431  cort 30949   chj 30952
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 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-in 3958  df-ss 3968
This theorem is referenced by:  3oalem5  31685
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