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Theorem wran 369
Description: Weak orthomodular law.
Hypothesis
Ref Expression
wran.1 (a == b) = 1
Assertion
Ref Expression
wran ((a ^ c) == (b ^ c)) = 1
Proof of Theorem wran
StepHypRef Expression
1 df-a 40 . . 3 (a ^ c) = (a' v c')'
2 df-a 40 . . 3 (b ^ c) = (b' v c')'
31, 22bi 99 . 2 ((a ^ c) == (b ^ c)) = ((a' v c')' == (b' v c')')
4 wran.1 . . . . 5 (a == b) = 1
54wr4 199 . . . 4 (a' == b') = 1
65wr5-2v 366 . . 3 ((a' v c') == (b' v c')) = 1
76wr4 199 . 2 ((a' v c')' == (b' v c')') = 1
83, 7ax-r2 36 1 ((a ^ c) == (b ^ c)) = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   == tb 5   v 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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