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Theorem gomaex3lem4 917
Description: Lemma for Godowski 6-var -> Mayet Example 3.
Hypothesis
Ref Expression
gomaex3lem4.9 p = ((a v b) ->1 (d v e)')'
Assertion
Ref Expression
gomaex3lem4 ((a v b) ^ (d v e)') =< p'
Proof of Theorem gomaex3lem4
StepHypRef Expression
1 leor 159 . 2 ((a v b) ^ (d v e)') =< ((a v b)' v ((a v b) ^ (d v e)'))
2 ax-a1 30 . . 3 ((a v b) ->1 (d v e)') = ((a v b) ->1 (d v e)')''
3 df-i1 44 . . . 4 ((a v b) ->1 (d v e)') = ((a v b)' v ((a v b) ^ (d v e)'))
43ax-r1 35 . . 3 ((a v b)' v ((a v b) ^ (d v e)')) = ((a v b) ->1 (d v e)')
5 gomaex3lem4.9 . . . 4 p = ((a v b) ->1 (d v e)')'
65ax-r4 37 . . 3 p' = ((a v b) ->1 (d v e)')''
72, 4, 63tr1 63 . 2 ((a v b)' v ((a v b) ^ (d v e)')) = p'
81, 7lbtr 139 1 ((a v b) ^ (d v e)') =< p'
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-i1 44  df-le1 130  df-le2 131
This theorem is referenced by:  gomaex3lem9  922
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