Description: Equality theorem for function value, analogous to fveq1 . (Contributed by AV, 4-Sep-2022)
Ref | Expression | ||
---|---|---|---|
Assertion | afv2eq1 | ⊢ ( 𝐹 = 𝐺 → ( 𝐹 '''' 𝐴 ) = ( 𝐺 '''' 𝐴 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id | ⊢ ( 𝐹 = 𝐺 → 𝐹 = 𝐺 ) | |
2 | eqidd | ⊢ ( 𝐹 = 𝐺 → 𝐴 = 𝐴 ) | |
3 | 1 2 | afv2eq12d | ⊢ ( 𝐹 = 𝐺 → ( 𝐹 '''' 𝐴 ) = ( 𝐺 '''' 𝐴 ) ) |