Theorem cadtru 1559

Description: The adder carry is true as soon as its first two inputs are the truth constant. (Contributed by Mario Carneiro, 4-Sep-2016.)

Assertion

Ref	Expression
cadtru	|- cadd ( T. , T. , ph )

Proof of Theorem cadtru

Step	Hyp	Ref	Expression
1		tru 1487	. 2 |- T.
2		cad11 1558	. 2 |- ( ( T. /\ T. ) -> cadd ( T. , T. , ph ) )
3	1, 1, 2	mp2an 708	1 |- cadd ( T. , T. , ph )

Syntax hints:   T. wtru 1484  caddwcad 1545

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 197  df-or 385  df-an 386  df-tru 1486  df-cad 1546

This theorem is referenced by: (None)