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Theorem oa3-1to5 993
 Description: Derivation of an equivalent of the second "universal" 3-OA U2 from an equivalent of the first "universal" 3-OA U1. This shows that U2 is redundant in a system containg U1. The hypothesis is theorem oal1 1000.
Hypothesis
Ref Expression
oa3-1to5.1
Assertion
Ref Expression
oa3-1to5

Proof of Theorem oa3-1to5
StepHypRef Expression
1 leid 148 . . . . 5
2 oa3-1to5.1 . . . . 5
31, 2lel2or 170 . . . 4
43lelan 167 . . 3
5 ax-a1 30 . . . . . . . 8
65ran 78 . . . . . . 7
76ax-r5 38 . . . . . 6
8 ax-a2 31 . . . . . 6
97, 8ax-r2 36 . . . . 5
10 u1lemab 610 . . . . 5
11 u1lemab 610 . . . . 5
129, 10, 113tr1 63 . . . 4
13 ancom 74 . . . 4
14 ancom 74 . . . 4
1512, 13, 143tr1 63 . . 3
164, 15lbtr 139 . 2
17 lear 161 . 2
1816, 17letr 137 1
 Colors of variables: term Syntax hints:   wle 2  wn 4   wo 6   wa 7   wi1 12 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-le1 130  df-le2 131  df-c1 132  df-c2 133
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