Theorem u1lemc1 680

Description: Commutation theorem for Sasaki implication.

Assertion

Ref	Expression
u1lemc1	a C (a ->1 b)

Proof of Theorem u1lemc1

Step	Hyp	Ref	Expression
1		comid 187	. . . 4 a C a
2	1	comcom2 183	. . 3 a C a'
3		comanr1 464	. . 3 a C (a ^ b)
4	2, 3	com2or 483	. 2 a C (a' v (a ^ b))
5		df-i1 44	. . 3 (a ->1 b) = (a' v (a ^ b))
6	5	ax-r1 35	. 2 (a' v (a ^ b)) = (a ->1 b)
7	4, 6	cbtr 182	1 a C (a ->1 b)

Syntax hints:   C wc 3  'wn 4   v wo 6   ^ wa 7   ->1 wi1 12

This theorem is referenced by:  u1lemc5 696  u12lembi 726  u1lem1 734  u1lem4 757  oas 925  oau 929

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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