Theorem ud1lem0a 247

Description: Introduce →₁ to the left.

Hypothesis

Ref	Expression
ud1lem0a.1	a = b

Assertion

Ref	Expression
ud1lem0a	(c →1 a) = (c →1 b)

Proof of Theorem ud1lem0a

Step	Hyp	Ref	Expression
1		ud1lem0a.1	. . . 4 a = b
2	1	lan 70	. . 3 (c ∩ a) = (c ∩ b)
3	2	lor 66	. 2 (c⊥ ∪ (c ∩ a)) = (c⊥ ∪ (c ∩ b))
4		df-i1 43	. 2 (c →1 a) = (c⊥ ∪ (c ∩ a))
5		df-i1 43	. 2 (c →1 b) = (c⊥ ∪ (c ∩ b))
6	3, 4, 5	3tr1 60	1 (c →1 a) = (c →1 b)

Syntax hints:   = wb 1  ^⊥ wn 4   ∪ wo 6   ∩ wa 7   →₁ wi1 13

This theorem is referenced by:  ud1lem0ab 249  wql1 285  nom42 319  ud1 577  u3lem13b 772  2oai1u 804  1oaiii 805  oa3to4lem1 925  oa3to4lem2 926  oa4to6lem1 940  oa4to6lem2 941  oa4to6lem3 942

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-i1 43

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