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Theorem 3oalem4 22244
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 3389 . 2  |-  ( ( _|_ `  B )  i^i  ( B  vH  A ) )  C_  ( _|_ `  B )
31, 2eqsstri 3208 1  |-  R  C_  ( _|_ `  B )
Colors of variables: wff set class
Syntax hints:    = wceq 1623    i^i cin 3151    C_ wss 3152   ` cfv 5255  (class class class)co 5858   _|_cort 21510    vH chj 21513
This theorem is referenced by:  3oalem5  22245
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-in 3159  df-ss 3166
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