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Theorem govar2 897
 Description: Lemma for converting n-variable to 2n-variable Godowski equations. (Contributed by NM, 19-Nov-1999.)
Hypotheses
Ref Expression
govar.1 ab
govar.2 bc
Assertion
Ref Expression
govar2 (ab) ≤ (c2 a)

Proof of Theorem govar2
StepHypRef Expression
1 govar.2 . . . 4 bc
2 govar.1 . . . . 5 ab
32lecon3 157 . . . 4 ba
41, 3ler2an 173 . . 3 b ≤ (ca )
54lelor 166 . 2 (ab) ≤ (a ∪ (ca ))
6 df-i2 45 . . 3 (c2 a) = (a ∪ (ca ))
76ax-r1 35 . 2 (a ∪ (ca )) = (c2 a)
85, 7lbtr 139 1 (ab) ≤ (c2 a)
 Colors of variables: term Syntax hints:   ≤ wle 2  ⊥ wn 4   ∪ 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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