Theorem cadtru 1649

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 1573	. 2 ⊢ ⊤
2		cad11 1645	. 2 ⊢ ((⊤ ∧ ⊤) → cadd(⊤, ⊤, 𝜑))
3	1, 1, 2	mp2an 704	1 ⊢ cadd(⊤, ⊤, 𝜑)

This proof depends on syntax axioms:  ⊤wtru 1570  caddwcad 1635

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1572  df-cad 1636

This theorem is used by: (None)