Description: Equality theorem for image. (Contributed by NM, 21-Dec-2008)
Ref | Expression | ||
---|---|---|---|
Hypothesis | imaeq1i.1 | ⊢ 𝐴 = 𝐵 | |
Assertion | imaeq2i | ⊢ ( 𝐶 “ 𝐴 ) = ( 𝐶 “ 𝐵 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imaeq1i.1 | ⊢ 𝐴 = 𝐵 | |
2 | imaeq2 | ⊢ ( 𝐴 = 𝐵 → ( 𝐶 “ 𝐴 ) = ( 𝐶 “ 𝐵 ) ) | |
3 | 1 2 | ax-mp | ⊢ ( 𝐶 “ 𝐴 ) = ( 𝐶 “ 𝐵 ) |