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Theorem gomaex3h7 908
 Description: Hypothesis for Godowski 6-var -> Mayet Example 3.
Hypotheses
Ref Expression
gomaex3h7.18 n = (p1 q)
gomaex3h7.19 u = (pq)
Assertion
Ref Expression
gomaex3h7 nu

Proof of Theorem gomaex3h7
StepHypRef Expression
1 leor 159 . . . 4 (pq) ≤ (p ∪ (pq))
2 df-i1 44 . . . . 5 (p1 q) = (p ∪ (pq))
32ax-r1 35 . . . 4 (p ∪ (pq)) = (p1 q)
41, 3lbtr 139 . . 3 (pq) ≤ (p1 q)
54lecon 154 . 2 (p1 q) ≤ (pq)
6 gomaex3h7.18 . 2 n = (p1 q)
7 gomaex3h7.19 . . 3 u = (pq)
87ax-r4 37 . 2 u = (pq)
95, 6, 8le3tr1 140 1 nu
 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-i1 44  df-le1 130  df-le2 131 This theorem is referenced by:  gomaex3lem5  918
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