Final answer:
The proof for the given logical statements makes use of modus ponens and modus tollens deductive reasoning, as well as the logical equivalency of universal statements to conditionals.
Step-by-step explanation:
The syntactic proof for the logical statements provided involves using deductible inferences such as modus ponens and modus tollens. For proposition 1. ⊢G (p→q)→(¬q→¬p), we can use modus tollens which starts with a conditional statement and infers the negation of the antecedent from the negation of the consequent. Similarly, for proposition 2. ⊢G (¬q→¬p)→(p→q), we also employ modus tollens to infer the truth of the consequent from the falsity of the antecedent.
The logical equivalence of universal statements to conditionals reveals that if a conditional statement is true, the inverse is also logically valid. Universal statements and their conditional counterparts help us to understand the logical flow and structure within arguments, thus aiding in proving the syntactic validity of the given propositions.