Theorem lem3.3.3 1051

Description: Equation 3.3 of [PavMeg1999] p. 9. (Contributed by Roy F. Longton, 3-Jul-05.)

Assertion

Ref	Expression
lem3.3.3	((a ==5 b) ->0 (a <->1 b)) = 1

Proof of Theorem lem3.3.3

Step	Hyp	Ref	Expression
1		df-i0 43	. 2 ((a ==5 b) ->0 (a <->1 b)) = ((a ==5 b)' v (a <->1 b))
2		df-b1 1047	. . 3 (a <->1 b) = ((a ->1 b) ^ (b ->1 a))
3	2	lor 70	. 2 ((a ==5 b)' v (a <->1 b)) = ((a ==5 b)' v ((a ->1 b) ^ (b ->1 a)))
4		lem3.3.3lem3 1050	. . 3 (a ==5 b) =< ((a ->1 b) ^ (b ->1 a))
5	4	sklem 230	. 2 ((a ==5 b)' v ((a ->1 b) ^ (b ->1 a))) = 1
6	1, 3, 5	3tr 65	1 ((a ==5 b) ->0 (a <->1 b)) = 1

Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7  1wt 8   ->0 wi0 11   ->1 wi1 12   ==5 wid5 22   <->1 wb1 24

This theorem is referenced by:  lem3.3.5 1054

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

This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-i0 43  df-i1 44  df-le1 130  df-le2 131  df-id5 1046  df-b1 1047

Copyright terms: Public domain