Question
Prove that the following arguments are standard by constructing metaphorical proof
$M \rightarrow N$
$N \rightarrow O$
$(M \rightarrow O) \rightarrow (N \rightarrow P)$
$(N \rightarrow P) \rightarrow Q$
$(Q\ v\ Z)\ \&\ Q$

Answer

$(1)\ M \rightarrow N$ $P$
$(2)\ N \rightarrow 0$ $P$
$(3)\ (M \rightarrow 0) \rightarrow (N \rightarrow P)$ $P$
$(4)\ (N \rightarrow P) \rightarrow Q$ $P/ (Q\ v\ Z)\ \&\ Q$
$(5)\ (M \rightarrow 0) \rightarrow Q$ $3, 4, HS$
$(6)\ M \rightarrow 0$ $1, 2, HS$
$(7)\ Q$ $5, 6, MP$
$(8)\ Q\ v\ Z$ $7,$ Add.
$(9)\ (Q\ v\ Z)\ \&\ Q$ $8, 7,$ Conj.

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