Rule of Implication/Sequent Form/Proof 1

Theorem

The Rule of Implication can be symbolised by the sequent:

$\ds \paren {p \vdash q}$

$\ds $

$\ds \vdash \ \ $

$\ds p \implies q$

$\ds $

$\paren {p \vdash q} \vdash p \implies q$
Line	Pool	Formula	Rule	Depends upon	Notes
1	1	$p$	Premise	(None)
2	1	$q$	By hypothesis	1	as $p \vdash q$
3	1	$p \implies q$	Rule of Implication: $\implies \II$	1 – 2	Assumption 1 has been discharged

$\blacksquare$