Theorem cadtru 1621

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(⊤, ⊤, 𝜑)

Proof of Theorem cadtru

Step	Hyp	Ref	Expression
1		tru 1541	. 2 ⊢ ⊤
2		cad11 1620	. 2 ⊢ ((⊤ ∧ ⊤) → cadd(⊤, ⊤, 𝜑))
3	1, 1, 2	mp2an 690	1 ⊢ cadd(⊤, ⊤, 𝜑)

Syntax hints:  ⊤wtru 1538  caddwcad 1607

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 209  df-an 399  df-or 844  df-tru 1540  df-cad 1608

This theorem is referenced by: (None)