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Theorem wom3 367
Description: Weak orthomodular law for study of weakly orthomodular lattices. (Contributed by NM, 13-Nov-1998.)
Hypothesis
Ref Expression
wom3.1 (ab) = 1
Assertion
Ref Expression
wom3 a ≤ ((ac) ≡ (bc))

Proof of Theorem wom3
StepHypRef Expression
1 le1 146 . 2 a ≤ 1
2 wom3.1 . . . . 5 (ab) = 1
32wr5-2v 366 . . . 4 ((ac) ≡ (bc)) = 1
43ax-r1 35 . . 3 1 = ((ac) ≡ (bc))
54bile 142 . 2 1 ≤ ((ac) ≡ (bc))
61, 5letr 137 1 a ≤ ((ac) ≡ (bc))
Colors of variables: term
Syntax hints:   = wb 1  wle 2  tb 5  wo 6  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: (None)
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