Theorem cadbi123i 1452

Description: Equality theorem for adder carry. (Contributed by Mario Carneiro, 4-Sep-2016.)

Hypotheses

Ref	Expression
hadbii.1
hadbii.2
hadbii.3

Assertion

Ref	Expression
cadbi123i

Proof of Theorem cadbi123i

Step	Hyp	Ref	Expression
1		hadbii.1	. . . 4
2	1	a1i 11	. . 3
3		hadbii.2	. . . 4
4	3	a1i 11	. . 3
5		hadbii.3	. . . 4
6	5	a1i 11	. . 3
7	2, 4, 6	cadbi123d 1450	. 2
8	7	trud 1404	1

Syntax hints:  <->wb 184  wtru 1396  caddwcad 1446

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-xor 1364  df-tru 1398  df-cad 1448