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Theorem 3oalem4 23128
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 3529 . 2  |-  ( ( _|_ `  B )  i^i  ( B  vH  A ) )  C_  ( _|_ `  B )
31, 2eqsstri 3346 1  |-  R  C_  ( _|_ `  B )
Colors of variables: wff set class
Syntax hints:    = wceq 1649    i^i cin 3287    C_ wss 3288   ` cfv 5421  (class class class)co 6048   _|_cort 22394    vH chj 22397
This theorem is referenced by:  3oalem5  23129
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-v 2926  df-in 3295  df-ss 3302
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