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Theorem wlecom 409
 Description: Comparable elements commute. Beran 84 2.3(iii) p. 40.
Hypothesis
Ref Expression
wlecom.1 (a2 b) = 1
Assertion
Ref Expression
wlecom C (a, b) = 1

Proof of Theorem wlecom
StepHypRef Expression
1 orabs 120 . . . . 5 (a ∪ (ab )) = a
21bi1 118 . . . 4 ((a ∪ (ab )) ≡ a) = 1
32wr1 197 . . 3 (a ≡ (a ∪ (ab ))) = 1
4 wlecom.1 . . . . . 6 (a2 b) = 1
54wdf2le2 386 . . . . 5 ((ab) ≡ a) = 1
65wr1 197 . . . 4 (a ≡ (ab)) = 1
76wr5-2v 366 . . 3 ((a ∪ (ab )) ≡ ((ab) ∪ (ab ))) = 1
83, 7wr2 371 . 2 (a ≡ ((ab) ∪ (ab ))) = 1
98wdf-c1 383 1 C (a, b) = 1
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7  1wt 8   ≤2 wle2 10   C wcmtr 29 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  df-cmtr 134 This theorem is referenced by:  wcomorr  412  wcoman1  413  wlem14  430  ska4  433
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