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Theorem gomaex3h4 905
 Description: Hypothesis for Godowski 6-var -> Mayet Example 3.
Hypotheses
Ref Expression
gomaex3h4.11 r = ((p1 q) ∩ (cd))
gomaex3h4.15 j = (cd)
gomaex3h4.16 k = r
Assertion
Ref Expression
gomaex3h4 jk

Proof of Theorem gomaex3h4
StepHypRef Expression
1 gomaex3h4.11 . . . 4 r = ((p1 q) ∩ (cd))
2 lear 161 . . . 4 ((p1 q) ∩ (cd)) ≤ (cd)
31, 2bltr 138 . . 3 r ≤ (cd)
43lecon 154 . 2 (cd)r
5 gomaex3h4.15 . 2 j = (cd)
6 gomaex3h4.16 . . 3 k = r
76ax-r4 37 . 2 k = r
84, 5, 7le3tr1 140 1 jk
 Colors of variables: term Syntax hints:   = wb 1   ≤ wle 2  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →1 wi1 12 This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38 This theorem depends on definitions:  df-a 40  df-le1 130  df-le2 131 This theorem is referenced by:  gomaex3lem5  918
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