Can you use green mana from a Forest to pay the colored mana requirement of a Phyrexian mana cost?

Phyrexian mana symbols (written as {G/P}, {U/P}, etc.) each represent a cost that can be paid in one of two ways: you may pay the corresponding colored mana, or you may pay 2 life. This is defined in CR 107.4f.

A Forest produces {G} (green mana). When you pay a {G/P} cost with that green mana, you are choosing the 'pay the colored mana' option. The Phyrexian symbol is fully satisfied, and you do not also pay 2 life — it is an either/or choice, not both (CR 107.4f, 601.2f).

You cannot, however, use green mana to pay a differently-colored Phyrexian symbol such as {U/P} or {R/P}. The mana's color must match the color of the Phyrexian symbol if you choose the mana-payment option.

Example: You cast Gut Shot ({R/P}) but have only a Forest. You cannot use that green mana to pay {R/P}'s colored option. You must instead pay 2 life to cast it. Conversely, if you cast a card with {G/P} in its cost, tapping your Forest for {G} pays that symbol cleanly with no life loss.

In short: green mana satisfies a green Phyrexian mana cost perfectly, giving you a free alternative to paying 2 life whenever your mana base supports it.