Theorem oveq12

Description: Equality theorem for operation value. (Contributed by NM, 16-Jul-1995)

	Ref	Expression
Assertion	oveq12	⊢ ( ( 𝐴 = 𝐵 ∧ 𝐶 = 𝐷 ) → ( 𝐴 𝐹 𝐶 ) = ( 𝐵 𝐹 𝐷 ) )

Proof

Step	Hyp	Ref	Expression
1		oveq1	⊢ ( 𝐴 = 𝐵 → ( 𝐴 𝐹 𝐶 ) = ( 𝐵 𝐹 𝐶 ) )
2		oveq2	⊢ ( 𝐶 = 𝐷 → ( 𝐵 𝐹 𝐶 ) = ( 𝐵 𝐹 𝐷 ) )
3	1 2	sylan9eq	⊢ ( ( 𝐴 = 𝐵 ∧ 𝐶 = 𝐷 ) → ( 𝐴 𝐹 𝐶 ) = ( 𝐵 𝐹 𝐷 ) )