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Theorem wom4 380
Description: Orthomodular law. Kalmbach 83 p. 22.
Hypothesis
Ref Expression
wom4.1 (a =<2 b) = 1
Assertion
Ref Expression
wom4 ((a v (a' ^ b)) == b) = 1
Proof of Theorem wom4
StepHypRef Expression
1 woml 211 . 2 ((a v (a' ^ (a v b))) == (a v b)) = 1
2 wom4.1 . . . . 5 (a =<2 b) = 1
32wdf-le2 379 . . . 4 ((a v b) == b) = 1
43wlan 370 . . 3 ((a' ^ (a v b)) == (a' ^ b)) = 1
54wlor 368 . 2 ((a v (a' ^ (a v b))) == (a v (a' ^ b))) = 1
61, 5, 3w3tr2 375 1 ((a v (a' ^ b)) == b) = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   == tb 5   v wo 6   ^ wa 7  1wt 8   =<2 wle2 10
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-le 129  df-le1 130  df-le2 131
This theorem is referenced by:  wom5  381  wcomlem  382  wcom3i  422
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