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Theorem 3oalem4 23172
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 3563 . 2  |-  ( ( _|_ `  B )  i^i  ( B  vH  A ) )  C_  ( _|_ `  B )
31, 2eqsstri 3380 1  |-  R  C_  ( _|_ `  B )
Colors of variables: wff set class
Syntax hints:    = wceq 1653    i^i cin 3321    C_ wss 3322   ` cfv 5457  (class class class)co 6084   _|_cort 22438    vH chj 22441
This theorem is referenced by:  3oalem5  23173
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-in 3329  df-ss 3336
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