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Theorem govar2 897
Description: Lemma for converting n-variable to 2n-variable Godowski equations.
Hypotheses
Ref Expression
govar.1 a =< b'
govar.2 b =< c'
Assertion
Ref Expression
govar2 (a v b) =< (c ->2 a)
Proof of Theorem govar2
StepHypRef Expression
1 govar.2 . . . 4 b =< c'
2 govar.1 . . . . 5 a =< b'
32lecon3 157 . . . 4 b =< a'
41, 3ler2an 173 . . 3 b =< (c' ^ a')
54lelor 166 . 2 (a v b) =< (a v (c' ^ a'))
6 df-i2 45 . . 3 (c ->2 a) = (a v (c' ^ a'))
76ax-r1 35 . 2 (a v (c' ^ a')) = (c ->2 a)
85, 7lbtr 139 1 (a v b) =< (c ->2 a)
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-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-i2 45  df-le1 130  df-le2 131
This theorem is referenced by:  gon2n  898  go2n4  899  go2n6  901
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