In her textbook for a course introducing mathematical proofs, Lakins initially presents only enough logic for students to be able to work with the propositional connectives
and the quantifiers, then focuses on getting students writing proofs as early as possible.
Below in the picture 2 the symbols [conjunction], [disjunction], [down arrow], |, [left right arrow], [[disjunction].bar]] stand for the propositional connectives
"conjunction", "disjunction (the not-excluding one)", "Peirce arrow (NOR)", "Sheffer stroke (NAND)", "equivalence", "strict disjunction (the excluding one)", respectively.
Indeed, The Connectives is nearly 1,500 pages of densely packed rumination over, well, the propositional connectives
The interplay of introduction and elimination rules for propositional connectives
is often seen as suggesting a distinguished role for intuitionistic logic.