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Theorem gomaex3lem1 914
 Description: Lemma for Godowski 6-var -> Mayet Example 3.
Hypothesis
Ref Expression
gomaex3lem1.3 cd
Assertion
Ref Expression
gomaex3lem1 (c ∪ (cd) ) = d

Proof of Theorem gomaex3lem1
StepHypRef Expression
1 comid 187 . . . 4 c C c
21comcom2 183 . . 3 c C c
3 gomaex3lem1.3 . . . 4 cd
43lecom 180 . . 3 c C d
52, 4fh3 471 . 2 (c ∪ (cd )) = ((cc ) ∩ (cd ))
6 anor3 90 . . 3 (cd ) = (cd)
76lor 70 . 2 (c ∪ (cd )) = (c ∪ (cd) )
8 ancom 74 . . 3 ((cc ) ∩ (cd )) = ((cd ) ∩ (cc ))
93df-le2 131 . . . . . 6 (cd ) = d
109ax-r1 35 . . . . 5 d = (cd )
11 df-t 41 . . . . 5 1 = (cc )
1210, 112an 79 . . . 4 (d ∩ 1) = ((cd ) ∩ (cc ))
1312ax-r1 35 . . 3 ((cd ) ∩ (cc )) = (d ∩ 1)
14 an1 106 . . 3 (d ∩ 1) = d
158, 13, 143tr 65 . 2 ((cc ) ∩ (cd )) = d
165, 7, 153tr2 64 1 (c ∪ (cd) ) = d
 Colors of variables: term Syntax hints:   = wb 1   ≤ wle 2  ⊥ wn 4   ∪ 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-r3 439 This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-le1 130  df-le2 131  df-c1 132  df-c2 133 This theorem is referenced by:  gomaex3lem7  920
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