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Theorem gomaex3h4 905
Description: Hypothesis for Godowski 6-var -> Mayet Example 3.
Hypotheses
Ref Expression
gomaex3h4.11 r = ((p' ->1 q)' ^ (c v d))
gomaex3h4.15 j = (c v d)'
gomaex3h4.16 k = r
Assertion
Ref Expression
gomaex3h4 j =< k'
Proof of Theorem gomaex3h4
StepHypRef Expression
1 gomaex3h4.11 . . . 4 r = ((p' ->1 q)' ^ (c v d))
2 lear 161 . . . 4 ((p' ->1 q)' ^ (c v d)) =< (c v d)
31, 2bltr 138 . . 3 r =< (c v d)
43lecon 154 . 2 (c v d)' =< r'
5 gomaex3h4.15 . 2 j = (c v d)'
6 gomaex3h4.16 . . 3 k = r
76ax-r4 37 . 2 k' = r'
84, 5, 7le3tr1 140 1 j =< k'
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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