逻辑学蕴涵命题中的「→」和数学中的「⇒」有什么区别和共同点？ 剩下的不想贴图了，自己去找 GTM 看。 那么有没有除了集合论和数理逻辑（如 GTM022）之外依旧频繁出现 \forall \exists 的教材呢？ 按照某人的说法，分析教材里面很喜欢的 \varepsilon-\delta 应该是一个很好的例子。 但是 比如说 025 Real and Abstract Analysis,
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
discrete mathematics - Proving (p → r) ∨ (q → r) ≡ (p ∧ q) → r . . . For the ( (p ∧ q) → r) → ( (p → r) ∨ (q → r)) part: This one was the main point of confusion (and what my question is all about) Proving a implication with a disjunction as the consequent was something I was unsure how to do (and what I've seen many other people have asked too online unsure about)
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