Theorem skmp3 245

Description: Soundness proof for KMP3. (Contributed by NM, 2-Nov-1997.)

Hypotheses

Ref	Expression
skmp3.1	a = 1
skmp3.2	(a →3 b) = 1

Assertion

Ref	Expression
skmp3	b = 1

Proof of Theorem skmp3

Step	Hyp	Ref	Expression
1		skmp3.1	. 2 a = 1
2		skmp3.2	. . 3 (a →3 b) = 1
3		ska15 244	. . 3 ((a →3 b)⊥ ∪ (a⊥ ∪ b)) = 1
4	2, 3	skr0 242	. 2 (a⊥ ∪ b) = 1
5	1, 4	skr0 242	1 b = 1

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ wo 6  1wt 8   →₃ wi3 14

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-i3 46  df-le1 130  df-le2 131

This theorem is referenced by:  i0i3tr  541  i3i0tr  542  i3th6  548