Theorem pm13.14

Description: Theorem *13.14 in WhiteheadRussell p. 178. (Contributed by Andrew Salmon, 3-Jun-2011)

	Ref	Expression
Assertion	pm13.14	|- ( ( [. A / x ]. ph /\ -. ph ) -> x =/= A )

Proof

Step	Hyp	Ref	Expression
1		sbceq1a	|- ( x = A -> ( ph <-> [. A / x ]. ph ) )
2	1	biimprcd	|- ( [. A / x ]. ph -> ( x = A -> ph ) )
3	2	necon3bd	|- ( [. A / x ]. ph -> ( -. ph -> x =/= A ) )
4	3	imp	|- ( ( [. A / x ]. ph /\ -. ph ) -> x =/= A )