Theorem ud1lem0ab 249

Description: Join both sides of hypotheses with ->1.

Hypotheses

Ref	Expression
ud1lem0ab.1	a = b
ud1lem0ab.2	c = d

Assertion

Ref	Expression
ud1lem0ab	(a ->1 c) = (b ->1 d)

Proof of Theorem ud1lem0ab

Step	Hyp	Ref	Expression
1		ud1lem0ab.1	. . 3 a = b
2	1	ud1lem0b 248	. 2 (a ->1 c) = (b ->1 c)
3		ud1lem0ab.2	. . 3 c = d
4	3	ud1lem0a 247	. 2 (b ->1 c) = (b ->1 d)
5	2, 4	ax-r2 35	1 (a ->1 c) = (b ->1 d)

Syntax hints:   = wb 1   ->1 wi1 13

This theorem is referenced by:  1oai1 803  gomaex3 904  oa3to4lem6 930  oa4to6 945

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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