Theorem i1i2con1 268

Description: Correspondence between Sasaki and Dishkant conditionals. (Contributed by NM, 28-Feb-1999.)

Assertion

Ref	Expression
i1i2con1	(a →1 b⊥ ) = (b →2 a⊥ )

Proof of Theorem i1i2con1

Step	Hyp	Ref	Expression
1		i1i2 266	. 2 (a →1 b⊥ ) = (b⊥ ⊥ →2 a⊥ )
2		ax-a1 30	. . . 4 b = b⊥ ⊥
3	2	ax-r1 35	. . 3 b⊥ ⊥ = b
4	3	ud2lem0b 259	. 2 (b⊥ ⊥ →2 a⊥ ) = (b →2 a⊥ )
5	1, 4	ax-r2 36	1 (a →1 b⊥ ) = (b →2 a⊥ )

Syntax hints:   = wb 1  ^⊥ wn 4   →₁ wi1 12   →₂ wi2 13

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-a 40  df-i1 44  df-i2 45

This theorem is referenced by: (None)