Description: Equality deduction for function value. (Contributed by NM, 29-May-1999)
Ref | Expression | ||
---|---|---|---|
Hypothesis | fveq2d.1 | ⊢ ( 𝜑 → 𝐴 = 𝐵 ) | |
Assertion | fveq2d | ⊢ ( 𝜑 → ( 𝐹 ‘ 𝐴 ) = ( 𝐹 ‘ 𝐵 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fveq2d.1 | ⊢ ( 𝜑 → 𝐴 = 𝐵 ) | |
2 | fveq2 | ⊢ ( 𝐴 = 𝐵 → ( 𝐹 ‘ 𝐴 ) = ( 𝐹 ‘ 𝐵 ) ) | |
3 | 1 2 | syl | ⊢ ( 𝜑 → ( 𝐹 ‘ 𝐴 ) = ( 𝐹 ‘ 𝐵 ) ) |