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Theorem gomaex3lem5 918
 Description: Lemma for Godowski 6-var -> Mayet Example 3.
Hypotheses
Ref Expression
gomaex3lem5.1 ab
gomaex3lem5.2 bc
gomaex3lem5.3 cd
gomaex3lem5.5 ef
gomaex3lem5.6 fa
gomaex3lem5.8 (((i2 g) ∩ (g2 y)) ∩ (((y2 w) ∩ (w2 n)) ∩ ((n2 k) ∩ (k2 i)))) ≤ (g2 i)
gomaex3lem5.9 p = ((ab) →1 (de) )
gomaex3lem5.10 q = ((ef) →1 (bc) )
gomaex3lem5.11 r = ((p1 q) ∩ (cd))
gomaex3lem5.12 g = a
gomaex3lem5.13 h = b
gomaex3lem5.14 i = c
gomaex3lem5.15 j = (cd)
gomaex3lem5.16 k = r
gomaex3lem5.17 m = (p1 q)
gomaex3lem5.18 n = (p1 q)
gomaex3lem5.19 u = (pq)
gomaex3lem5.20 w = q
gomaex3lem5.21 x = q
gomaex3lem5.22 y = (ef)
gomaex3lem5.23 z = f
Assertion
Ref Expression
gomaex3lem5 (((gh) ∩ (ij)) ∩ (((km) ∩ (nu)) ∩ ((wx) ∩ (yz)))) ≤ (hi)

Proof of Theorem gomaex3lem5
StepHypRef Expression
1 gomaex3lem5.1 . . 3 ab
2 gomaex3lem5.12 . . 3 g = a
3 gomaex3lem5.13 . . 3 h = b
41, 2, 3gomaex3h1 902 . 2 gh
5 gomaex3lem5.2 . . 3 bc
6 gomaex3lem5.14 . . 3 i = c
75, 3, 6gomaex3h2 903 . 2 hi
8 gomaex3lem5.15 . . 3 j = (cd)
96, 8gomaex3h3 904 . 2 ij
10 gomaex3lem5.11 . . 3 r = ((p1 q) ∩ (cd))
11 gomaex3lem5.16 . . 3 k = r
1210, 8, 11gomaex3h4 905 . 2 jk
13 gomaex3lem5.17 . . 3 m = (p1 q)
1410, 11, 13gomaex3h5 906 . 2 km
15 gomaex3lem5.18 . . 3 n = (p1 q)
1613, 15gomaex3h6 907 . 2 mn
17 gomaex3lem5.19 . . 3 u = (pq)
1815, 17gomaex3h7 908 . 2 nu
19 gomaex3lem5.20 . . 3 w = q
2017, 19gomaex3h8 909 . 2 uw
21 gomaex3lem5.21 . . 3 x = q
2219, 21gomaex3h9 910 . 2 wx
23 gomaex3lem5.10 . . 3 q = ((ef) →1 (bc) )
24 gomaex3lem5.22 . . 3 y = (ef)
2523, 21, 24gomaex3h10 911 . 2 xy
26 gomaex3lem5.23 . . 3 z = f
2724, 26gomaex3h11 912 . 2 yz
28 gomaex3lem5.6 . . 3 fa
2928, 2, 26gomaex3h12 913 . 2 zg
30 gomaex3lem5.8 . 2 (((i2 g) ∩ (g2 y)) ∩ (((y2 w) ∩ (w2 n)) ∩ ((n2 k) ∩ (k2 i)))) ≤ (g2 i)
314, 7, 9, 12, 14, 16, 18, 20, 22, 25, 27, 29, 30go2n6 901 1 (((gh) ∩ (ij)) ∩ (((km) ∩ (nu)) ∩ ((wx) ∩ (yz)))) ≤ (hi)
 Colors of variables: term Syntax hints:   = wb 1   ≤ wle 2  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →1 wi1 12   →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-i1 44  df-i2 45  df-le1 130  df-le2 131  df-c1 132  df-c2 133 This theorem is referenced by:  gomaex3lem6  919
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