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Theorem str 189
Description: Strengthening rule.
Hypotheses
Ref Expression
str.1 a =< (b v c)
str.2 (a ^ (b v c)) =< b
Assertion
Ref Expression
str a =< b

Proof of Theorem str
StepHypRef Expression
1 id 59 . . . 4 a = a
21bile 142 . . 3 a =< a
3 str.1 . . 3 a =< (b v c)
42, 3ler2an 173 . 2 a =< (a ^ (b v c))
5 str.2 . 2 (a ^ (b v c)) =< b
64, 5letr 137 1 a =< b
Colors of variables: term
Syntax hints:   =< wle 2   v wo 6   ^ wa 7
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-le1 130  df-le2 131
This theorem is referenced by: (None)
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