This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem oveq123i

Description: Equality inference for operation value. (Contributed by FL, 11-Jul-2010)

Ref Expression
Hypotheses oveq123i.1 ⊢ 𝐴 = 𝐶
oveq123i.2 ⊢ 𝐵 = 𝐷
oveq123i.3 ⊢ 𝐹 = 𝐺
Assertion oveq123i ( 𝐴 𝐹 𝐵 ) = ( 𝐶 𝐺 𝐷 )

Proof

Step Hyp Ref Expression
1 oveq123i.1 ⊢ 𝐴 = 𝐶
2 oveq123i.2 ⊢ 𝐵 = 𝐷
3 oveq123i.3 ⊢ 𝐹 = 𝐺
4 1 2 oveq12i ⊢ ( 𝐴 𝐹 𝐵 ) = ( 𝐶 𝐹 𝐷 )
5 3 oveqi ⊢ ( 𝐶 𝐹 𝐷 ) = ( 𝐶 𝐺 𝐷 )
6 4 5 eqtri ⊢ ( 𝐴 𝐹 𝐵 ) = ( 𝐶 𝐺 𝐷 )