Lemma 1.1.4.
Assuming that:
Γ
⊢
IPC
φ
ψ
a proposition
Then
Γ
,
ψ
⊢
IPC
φ
. Moreover, if
p
is a primitive proposition and
ψ
is any proposition, then
Γ
[
p
:
=
ψ
]
⊢
IPC
φ
[
p
:
=
ψ
]
.