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Theorem gomaex3h5 906
Description: Hypothesis for Godowski 6-var -> Mayet Example 3.
Hypotheses
Ref Expression
gomaex3h5.11 r = ((p' ->1 q)' ^ (c v d))
gomaex3h5.16 k = r
gomaex3h5.17 m = (p' ->1 q)
Assertion
Ref Expression
gomaex3h5 k =< m'
Proof of Theorem gomaex3h5
StepHypRef Expression
1 gomaex3h5.11 . . 3 r = ((p' ->1 q)' ^ (c v d))
2 lea 160 . . 3 ((p' ->1 q)' ^ (c v d)) =< (p' ->1 q)'
31, 2bltr 138 . 2 r =< (p' ->1 q)'
4 gomaex3h5.16 . 2 k = r
5 gomaex3h5.17 . . 3 m = (p' ->1 q)
65ax-r4 37 . 2 m' = (p' ->1 q)'
73, 4, 6le3tr1 140 1 k =< m'
Colors of variables: term
Syntax hints:   = wb 1   =< wle 2  'wn 4   v 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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