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Theorem gomaex3h8 909
Description: Hypothesis for Godowski 6-var -> Mayet Example 3.
Hypotheses
Ref Expression
gomaex3h8.19 u = (p' ^ q)
gomaex3h8.20 w = q'
Assertion
Ref Expression
gomaex3h8 u =< w'

Proof of Theorem gomaex3h8
StepHypRef Expression
1 lear 161 . . 3 (p' ^ q) =< q
2 ax-a1 30 . . 3 q = q''
31, 2lbtr 139 . 2 (p' ^ q) =< q''
4 gomaex3h8.19 . 2 u = (p' ^ q)
5 gomaex3h8.20 . . 3 w = q'
65ax-r4 37 . 2 w' = q''
73, 4, 6le3tr1 140 1 u =< w'
Colors of variables: term
Syntax hints:   = wb 1   =< wle 2  'wn 4   ^ wa 7
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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