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Theorem gon2n 898
 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
gon2n.3 ((c2 a) ∩ d) ≤ (a2 c)
gon2n.4 ed
Assertion
Ref Expression
gon2n ((ab) ∩ e) ≤ (bc)

Proof of Theorem gon2n
StepHypRef Expression
1 lea 160 . . 3 ((ab) ∩ e) ≤ (ab)
2 govar.1 . . . . . 6 ab
3 govar.2 . . . . . 6 bc
42, 3govar2 897 . . . . 5 (ab) ≤ (c2 a)
5 gon2n.4 . . . . 5 ed
64, 5le2an 169 . . . 4 ((ab) ∩ e) ≤ ((c2 a) ∩ d)
7 gon2n.3 . . . 4 ((c2 a) ∩ d) ≤ (a2 c)
86, 7letr 137 . . 3 ((ab) ∩ e) ≤ (a2 c)
91, 8ler2an 173 . 2 ((ab) ∩ e) ≤ ((ab) ∩ (a2 c))
102, 3govar 896 . 2 ((ab) ∩ (a2 c)) ≤ (bc)
119, 10letr 137 1 ((ab) ∩ e) ≤ (bc)
 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-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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