Theorem an1r 99

Description: Conjunction with 1.

Assertion

Ref	Expression
an1r	(1 ∩ a) = a

Proof of Theorem an1r

Step	Hyp	Ref	Expression
1		ancom 68	. 2 (1 ∩ a) = (a ∩ 1)
2		an1 98	. 2 (a ∩ 1) = a
3	1, 2	ax-r2 35	1 (1 ∩ a) = a

Syntax hints:   = wb 1   ∩ wa 7  1wt 9

This theorem is referenced by:  ud3lem1c 550  ud3lem3 558  ud5lem1 571  i2i1i1 782

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37

This theorem depends on definitions:  df-a 39  df-t 40  df-f 41

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