Theorem ud2lem0b 251

Description: Introduce →₂ to the right.

Hypothesis

Ref	Expression
ud2lem0a.1	a = b

Assertion

Ref	Expression
ud2lem0b	(a →2 c) = (b →2 c)

Proof of Theorem ud2lem0b

Step	Hyp	Ref	Expression
1		ud2lem0a.1	. . . . 5 a = b
2	1	ax-r4 36	. . . 4 a⊥ = b⊥
3	2	ran 71	. . 3 (a⊥ ∩ c⊥ ) = (b⊥ ∩ c⊥ )
4	3	lor 66	. 2 (c ∪ (a⊥ ∩ c⊥ )) = (c ∪ (b⊥ ∩ c⊥ ))
5		df-i2 44	. 2 (a →2 c) = (c ∪ (a⊥ ∩ c⊥ ))
6		df-i2 44	. 2 (b →2 c) = (c ∪ (b⊥ ∩ c⊥ ))
7	4, 5, 6	3tr1 60	1 (a →2 c) = (b →2 c)

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

This theorem is referenced by:  i2i1 259  i1i2con1 260  ud2 578  2oath1i1 809

This theorem was proved from axioms:  ax-a2 30  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37

This theorem depends on definitions:  df-a 39  df-i2 44

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