Theorem pm11.62

Description: Theorem *11.62 in WhiteheadRussell p. 166. Importation combined with the rearrangement with quantifiers. (Contributed by Andrew Salmon, 24-May-2011)

	Ref	Expression
Assertion	pm11.62	|- ( A. x A. y ( ( ph /\ ps ) -> ch ) <-> A. x ( ph -> A. y ( ps -> ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		impexp	|- ( ( ( ph /\ ps ) -> ch ) <-> ( ph -> ( ps -> ch ) ) )
2	1	albii	|- ( A. y ( ( ph /\ ps ) -> ch ) <-> A. y ( ph -> ( ps -> ch ) ) )
3		19.21v	|- ( A. y ( ph -> ( ps -> ch ) ) <-> ( ph -> A. y ( ps -> ch ) ) )
4	2 3	bitri	|- ( A. y ( ( ph /\ ps ) -> ch ) <-> ( ph -> A. y ( ps -> ch ) ) )
5	4	albii	|- ( A. x A. y ( ( ph /\ ps ) -> ch ) <-> A. x ( ph -> A. y ( ps -> ch ) ) )