Theorem bj-alanim 32596

Description: Closed form of alanimi 1744. (Contributed by BJ, 6-May-2019.)

Assertion

Ref	Expression
bj-alanim	|- ( A. x ( ( ph /\ ps ) -> ch ) -> ( ( A. x ph /\ A. x ps ) -> A. x ch ) )

Proof of Theorem bj-alanim

Step	Hyp	Ref	Expression
1		pm3.3 460	. . . 4 |- ( ( ( ph /\ ps ) -> ch ) -> ( ph -> ( ps -> ch ) ) )
2	1	alimi 1739	. . 3 |- ( A. x ( ( ph /\ ps ) -> ch ) -> A. x ( ph -> ( ps -> ch ) ) )
3		al2im 1742	. . 3 |- ( A. x ( ph -> ( ps -> ch ) ) -> ( A. x ph -> ( A. x ps -> A. x ch ) ) )
4	2, 3	syl 17	. 2 |- ( A. x ( ( ph /\ ps ) -> ch ) -> ( A. x ph -> ( A. x ps -> A. x ch ) ) )
5	4	impd 447	1 |- ( A. x ( ( ph /\ ps ) -> ch ) -> ( ( A. x ph /\ A. x ps ) -> A. x ch ) )

Syntax hints:   -> wi 4   /\ wa 384   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by: (None)