Let A and B be any propositions expressible in the propositional calculus notation.
Show that A $\vdash$ B is provable by the rules of propositional calculus if and only if it is provable that $\vdash$ (A $\rightarrow$ B).
In proving that if $\vdash$ (A $\rightarrow$ B) is provable, then A $\vdash$ B is provable, I have the following:
1 (1) A $\rightarrow$ B $\:\:\:\:$ A
2 (2) A $\:\:\:\:\:\:\:\:\:\:\:\:$A
1,2 (3) B $\:\:\:\:\:\:\:\:\:\:\:\:$MP 1, 2
$\therefore$ A $\vdash$ B is provable.
Is this correct or am I missing something?