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Theorem u1lem12 781
Description: Lemma used in study of orthoarguesian law. Equation 4.12 of [MegPav2000] p. 23.
Assertion
Ref Expression
u1lem12 ((a ->1 b) ->1 b) = (a' ->1 b)
Proof of Theorem u1lem12
StepHypRef Expression
1 ax-a1 30 . . . 4 a = a''
21ud1lem0b 256 . . 3 (a ->1 b) = (a'' ->1 b)
32ud1lem0b 256 . 2 ((a ->1 b) ->1 b) = ((a'' ->1 b) ->1 b)
4 u1lem11 780 . 2 ((a'' ->1 b) ->1 b) = (a' ->1 b)
53, 4ax-r2 36 1 ((a ->1 b) ->1 b) = (a' ->1 b)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   ->1 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
This theorem is referenced by:  sac  835  oa4gto4u  976  lem4.6.4  1084
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