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Theorem 3oalem4 22260
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 3402 . 2  |-  ( ( _|_ `  B )  i^i  ( B  vH  A ) )  C_  ( _|_ `  B )
31, 2eqsstri 3221 1  |-  R  C_  ( _|_ `  B )
Colors of variables: wff set class
Syntax hints:    = wceq 1632    i^i cin 3164    C_ wss 3165   ` cfv 5271  (class class class)co 5874   _|_cort 21526    vH chj 21529
This theorem is referenced by:  3oalem5  22261
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-in 3172  df-ss 3179
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