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Theorem 1oaiii 823
 Description: OML analog to orthoarguesian law of Godowski/Greechie, Eq. III with instead of .
Assertion
Ref Expression
1oaiii

Proof of Theorem 1oaiii
StepHypRef Expression
1 anass 76 . . . . 5
2 anidm 111 . . . . . 6
32lan 77 . . . . 5
41, 3ax-r2 36 . . . 4
54ax-r1 35 . . 3
6 1oa 820 . . . 4
76leran 153 . . 3
85, 7bltr 138 . 2
9 anass 76 . . . . 5
10 ancom 74 . . . . . . . . . 10
1110ud1lem0a 255 . . . . . . . . 9
12 ax-a2 31 . . . . . . . . . 10
1312ud1lem0b 256 . . . . . . . . 9
1411, 13ax-r2 36 . . . . . . . 8
1514ran 78 . . . . . . 7
1615, 2ax-r2 36 . . . . . 6
1716lan 77 . . . . 5
189, 17ax-r2 36 . . . 4
1918ax-r1 35 . . 3
20 1oa 820 . . . 4
2120leran 153 . . 3
2219, 21bltr 138 . 2
238, 22lebi 145 1
 Colors of variables: term Syntax hints:   wb 1   wo 6   wa 7   wi1 12   wi2 13 This theorem is referenced by:  1oaii  824 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
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