Theorem al2imVD 39098

Description: Virtual deduction proof of al2im 1742. The following user's proof is completed by invoking mmj2's unify command and using mmj2's StepSelector to pick all remaining steps of the Metamath proof.

1::	|- (. A. x ( ph -> ( ps -> ch ) ) ->. A. x ( ph -> ( ps -> ch ) ) ).
2:1,?: e1a 38852	|- (. A. x ( ph -> ( ps -> ch ) ) ->. ( A. x ph -> A. x ( ps -> ch ) ) ).
3::	|- ( A. x ( ps -> ch ) -> ( A. x ps -> A. x ch ) )
4:2,3,?: e10 38919	|- (. A. x ( ph -> ( ps -> ch ) ) ->. ( A. x ph -> ( A. x ps -> A. x ch ) ) ).
qed:4:	|- ( A. x ( ph -> ( ps -> ch ) ) -> ( A. x ph -> ( A. x ps -> A. x ch ) ) )

(Contributed by Alan Sare, 31-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
al2imVD	|- ( A. x ( ph -> ( ps -> ch ) ) -> ( A. x ph -> ( A. x ps -> A. x ch ) ) )

Proof of Theorem al2imVD

Step	Hyp	Ref	Expression
1		idn1 38790	. . . 4 |- (. A. x ( ph -> ( ps -> ch ) ) ->. A. x ( ph -> ( ps -> ch ) ) ).
2		alim 1738	. . . 4 |- ( A. x ( ph -> ( ps -> ch ) ) -> ( A. x ph -> A. x ( ps -> ch ) ) )
3	1, 2	e1a 38852	. . 3 |- (. A. x ( ph -> ( ps -> ch ) ) ->. ( A. x ph -> A. x ( ps -> ch ) ) ).
4		alim 1738	. . 3 |- ( A. x ( ps -> ch ) -> ( A. x ps -> A. x ch ) )
5		imim1 83	. . 3 |- ( ( A. x ph -> A. x ( ps -> ch ) ) -> ( ( A. x ( ps -> ch ) -> ( A. x ps -> A. x ch ) ) -> ( A. x ph -> ( A. x ps -> A. x ch ) ) ) )
6	3, 4, 5	e10 38919	. 2 |- (. A. x ( ph -> ( ps -> ch ) ) ->. ( A. x ph -> ( A. x ps -> A. x ch ) ) ).
7	6	in1 38787	1 |- ( A. x ( ph -> ( ps -> ch ) ) -> ( A. x ph -> ( A. x ps -> A. x ch ) ) )

Syntax hints:   -> wi 4   A.wal 1481

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

This theorem depends on definitions:  df-bi 197  df-vd1 38786

This theorem is referenced by: (None)