Theorem u3lem12 788

Description: Lemma for unified implication study. (Contributed by NM, 18-Jan-1998.)

Assertion

Ref	Expression
u3lem12	(a →3 (a →3 b⊥ ))⊥ = (a ∩ b)

Proof of Theorem u3lem12

Step	Hyp	Ref	Expression
1		lem4 511	. . 3 (a →3 (a →3 b⊥ )) = (a⊥ ∪ b⊥ )
2	1	ax-r4 37	. 2 (a →3 (a →3 b⊥ ))⊥ = (a⊥ ∪ b⊥ )⊥
3		df-a 40	. . 3 (a ∩ b) = (a⊥ ∪ b⊥ )⊥
4	3	ax-r1 35	. 2 (a⊥ ∪ b⊥ )⊥ = (a ∩ b)
5	2, 4	ax-r2 36	1 (a →3 (a →3 b⊥ ))⊥ = (a ∩ b)

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ wo 6   ∩ wa 7   →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  ax-r3 439

This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i3 46  df-le1 130  df-le2 131  df-c1 132  df-c2 133

This theorem is referenced by: (None)