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Metamath Proof Explorer

Theorem fveq2i

Description: Equality inference for function value. (Contributed by NM, 28-Jul-1999)

Ref Expression
Hypothesis fveq2i.1 ⊢ 𝐴 = 𝐵
Assertion fveq2i ( 𝐹 ‘ 𝐴 ) = ( 𝐹 ‘ 𝐵 )

Proof

Step Hyp Ref Expression
1 fveq2i.1 ⊢ 𝐴 = 𝐵
2 fveq2 ⊢ ( 𝐴 = 𝐵 → ( 𝐹 ‘ 𝐴 ) = ( 𝐹 ‘ 𝐵 ) )
3 1 2 ax-mp ⊢ ( 𝐹 ‘ 𝐴 ) = ( 𝐹 ‘ 𝐵 )