Description: If (at least) two inputs are true, then the adder carry is true. (Contributed by Mario Carneiro, 4-Sep-2016)
Ref | Expression | ||
---|---|---|---|
Assertion | cad11 | ⊢ ( ( 𝜑 ∧ 𝜓 ) → cadd ( 𝜑 , 𝜓 , 𝜒 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orc | ⊢ ( ( 𝜑 ∧ 𝜓 ) → ( ( 𝜑 ∧ 𝜓 ) ∨ ( 𝜒 ∧ ( 𝜑 ⊻ 𝜓 ) ) ) ) | |
2 | df-cad | ⊢ ( cadd ( 𝜑 , 𝜓 , 𝜒 ) ↔ ( ( 𝜑 ∧ 𝜓 ) ∨ ( 𝜒 ∧ ( 𝜑 ⊻ 𝜓 ) ) ) ) | |
3 | 1 2 | sylibr | ⊢ ( ( 𝜑 ∧ 𝜓 ) → cadd ( 𝜑 , 𝜓 , 𝜒 ) ) |