Difference between implies and turnstile symbols (→ and ⊢) So this would imply to me that → and ⊢ are equivalent, but it's idiomatic to use ⊢ for metamathematics, and → otherwise Or, more concretely: (A → B) → (C → D) is the same as (A → B) ⊢ (C → D), but the second option is considered more idiomatic readable as we differentiate the smaller connections from the larger ones
How to make a formal proof with A → (B ∨ C) ⊢ (A → B) ∨ (A → C) Here is what I've got so far: I feel like I need an indirect proof for this and so I need to prove a contradiction with one of line 4 or 5 I'm not sure how to approach it Any hints that can help