Description: Equality deduction for function value. (Contributed by NM, 2-Sep-2003)
Ref | Expression | ||
---|---|---|---|
Hypothesis | fveq1d.1 | ⊢ ( 𝜑 → 𝐹 = 𝐺 ) | |
Assertion | fveq1d | ⊢ ( 𝜑 → ( 𝐹 ‘ 𝐴 ) = ( 𝐺 ‘ 𝐴 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fveq1d.1 | ⊢ ( 𝜑 → 𝐹 = 𝐺 ) | |
2 | fveq1 | ⊢ ( 𝐹 = 𝐺 → ( 𝐹 ‘ 𝐴 ) = ( 𝐺 ‘ 𝐴 ) ) | |
3 | 1 2 | syl | ⊢ ( 𝜑 → ( 𝐹 ‘ 𝐴 ) = ( 𝐺 ‘ 𝐴 ) ) |