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Theorem wran 369
 Description: Weak orthomodular law.
Hypothesis
Ref Expression
wran.1 (ab) = 1
Assertion
Ref Expression
wran ((ac) ≡ (bc)) = 1

Proof of Theorem wran
StepHypRef Expression
1 df-a 40 . . 3 (ac) = (ac )
2 df-a 40 . . 3 (bc) = (bc )
31, 22bi 99 . 2 ((ac) ≡ (bc)) = ((ac ) ≡ (bc ) )
4 wran.1 . . . . 5 (ab) = 1
54wr4 199 . . . 4 (ab ) = 1
65wr5-2v 366 . . 3 ((ac ) ≡ (bc )) = 1
76wr4 199 . 2 ((ac ) ≡ (bc ) ) = 1
83, 7ax-r2 36 1 ((ac) ≡ (bc)) = 1
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ≡ tb 5   ∪ wo 6   ∩ wa 7  1wt 8 This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-wom 361 This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i1 44  df-i2 45  df-le1 130  df-le2 131 This theorem is referenced by:  wlan  370  wr2  371  w2an  373  wcomlem  382  wlel  392  wleran  394  wbctr  410  wcom3i  422  wfh2  424
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