Theorem an1r 107

Description: Conjunction with 1.

Assertion

Ref	Expression
an1r	(1 ^ a) = a

Proof of Theorem an1r

Step	Hyp	Ref	Expression
1		ancom 74	. 2 (1 ^ a) = (a ^ 1)
2		an1 106	. 2 (a ^ 1) = a
3	1, 2	ax-r2 36	1 (1 ^ a) = a

Syntax hints:   = wb 1   ^ wa 7  1wt 8

This theorem is referenced by:  ud3lem1c 568  ud3lem3 576  ud5lem1 589  i2i1i1 800  lem3.3.7i1e1 1060  lem3.3.7i1e2 1061  lem3.3.7i2e1 1063  lem3.3.7i2e2 1064  lem3.3.7i3e2 1067  lem3.3.7i4e2 1070  lem4.6.6i1j3 1092  dplem15a 1148

This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38

This theorem depends on definitions:  df-a 40  df-t 41  df-f 42

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