Description: Equality deduction for operation value. (Contributed by NM, 9-Sep-2006)
Ref | Expression | ||
---|---|---|---|
Hypothesis | oveq1d.1 | ⊢ ( 𝜑 → 𝐴 = 𝐵 ) | |
Assertion | oveqd | ⊢ ( 𝜑 → ( 𝐶 𝐴 𝐷 ) = ( 𝐶 𝐵 𝐷 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq1d.1 | ⊢ ( 𝜑 → 𝐴 = 𝐵 ) | |
2 | oveq | ⊢ ( 𝐴 = 𝐵 → ( 𝐶 𝐴 𝐷 ) = ( 𝐶 𝐵 𝐷 ) ) | |
3 | 1 2 | syl | ⊢ ( 𝜑 → ( 𝐶 𝐴 𝐷 ) = ( 𝐶 𝐵 𝐷 ) ) |