Theorem 2vwomr1a 345

Description: 2-variable WOML rule.

Hypothesis

Ref	Expression
2vwomr1a.1	(a →1 b) = 1

Assertion

Ref	Expression
2vwomr1a	(a →2 b) = 1

Proof of Theorem 2vwomr1a

Step	Hyp	Ref	Expression
1		df-i2 44	. 2 (a →2 b) = (b ∪ (a⊥ ∩ b⊥ ))
2		df-i1 43	. . . . 5 (a →1 b) = (a⊥ ∪ (a ∩ b))
3	2	ax-r1 34	. . . 4 (a⊥ ∪ (a ∩ b)) = (a →1 b)
4		2vwomr1a.1	. . . 4 (a →1 b) = 1
5	3, 4	ax-r2 35	. . 3 (a⊥ ∪ (a ∩ b)) = 1
6	5	ax-wom 343	. 2 (b ∪ (a⊥ ∩ b⊥ )) = 1
7	1, 6	ax-r2 35	1 (a →2 b) = 1

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ wo 6   ∩ wa 7  1wt 9   →₁ wi1 13   →₂ wi2 14

This theorem is referenced by:  wr5-2v 348

This theorem was proved from axioms:  ax-r1 34  ax-r2 35  ax-wom 343

This theorem depends on definitions:  df-i1 43  df-i2 44

metamath.org