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Spells you cast that share multiple card types with the exiled card still cost just less to cast. They don't get a greater cost reduction.
Semblance Anvil takes the total cost to cast a spell into account, not just its mana cost. This includes additional costs (such as kicker) and alternative costs (such as evoke). It also includes cost increases from other sources (such as Lodestone Golem's ability).
Semblance Anvil's cost reduction effect is mandatory.
Semblance Anvil can reduce the amount you pay for a spell's cost that includes . For example, Blaze is a sorcery that costs . If the card exiled with Semblance Anvil is a sorcery, and you want to cast Blaze with X equal to 5, you'll have to pay only . This is true even if the ability states that must be paid with a certain color of mana (as Drain Life does).
Semblance Anvil won't affect the part of a spell's cost represented by colored mana symbols. For example, a spell that normally costs to cast would cost if it shared a card type with the exiled card.
Artifact, battle, creature, enchantment, instant, kindred, planeswalker, and sorcery are card types.
