# Section 2.5: Problem 1 Solution

Working problems is a crucial part of learning mathematics. No one can learn... merely by poring over the definitions, theorems, and examples that are worked out in the text. One must work part of it out for oneself. To provide that opportunity is the purpose of the exercises.

James R. Munkres

(Semantical rule EI) Assume that the constant symbol
does not occur in
,
, or
, and that
. Show (without using the soundness and completeness theorems) that
.

The “without using the soundness and completeness theorems” refers to Corollary 24H (Rule EI).

iff [for any
and
such that
and
,
] iff [for any
and
such that
and
,
] iff [for any
and
such that
and
,
] iff [for any
and
such that
and
,
] iff (
due to
not occurring in
,
or
) [for any
and
such that
and
, for all
,
] iff [for any
and
such that
and
,
] iff [for any
and
such that
and
,
] iff
.