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Theorem gon2n 898
Description: Lemma for converting n-variable to 2n-variable Godowski equations.
Hypotheses
Ref Expression
govar.1 a =< b'
govar.2 b =< c'
gon2n.3 ((c ->2 a) ^ d) =< (a ->2 c)
gon2n.4 e =< d
Assertion
Ref Expression
gon2n ((a v b) ^ e) =< (b v c)
Proof of Theorem gon2n
StepHypRef Expression
1 lea 160 . . 3 ((a v b) ^ e) =< (a v b)
2 govar.1 . . . . . 6 a =< b'
3 govar.2 . . . . . 6 b =< c'
42, 3govar2 897 . . . . 5 (a v b) =< (c ->2 a)
5 gon2n.4 . . . . 5 e =< d
64, 5le2an 169 . . . 4 ((a v b) ^ e) =< ((c ->2 a) ^ d)
7 gon2n.3 . . . 4 ((c ->2 a) ^ d) =< (a ->2 c)
86, 7letr 137 . . 3 ((a v b) ^ e) =< (a ->2 c)
91, 8ler2an 173 . 2 ((a v b) ^ e) =< ((a v b) ^ (a ->2 c))
102, 3govar 896 . 2 ((a v b) ^ (a ->2 c)) =< (b v c)
119, 10letr 137 1 ((a v b) ^ e) =< (b v c)
Colors of variables: term
Syntax hints:   =< wle 2  'wn 4   v wo 6   ^ wa 7   ->2 wi2 13
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-r3 439
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i2 45  df-le1 130  df-le2 131  df-c1 132  df-c2 133
This theorem is referenced by:  go2n4  899  go2n6  901
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