Theorem syl5impVD 39099

Description: Virtual deduction proof of syl5imp 38718. 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::	|- (. ( ph -> ( ps -> ch ) ) ->. ( ph -> ( ps -> ch ) ) ).
2:1,?: e1a 38852	|- (. ( ph -> ( ps -> ch ) ) ->. ( ps -> ( ph -> ch ) ) ).
3::	|- (. ( ph -> ( ps -> ch ) ) ,. ( th -> ps ) ->. ( th -> ps ) ).
4:3,2,?: e21 38957	|- (. ( ph -> ( ps -> ch ) ) ,. ( th -> ps ) ->. ( th -> ( ph -> ch ) ) ).
5:4,?: e2 38856	|- (. ( ph -> ( ps -> ch ) ) ,. ( th -> ps ) ->. ( ph -> ( th -> ch ) ) ).
6:5:	|- (. ( ph -> ( ps -> ch ) ) ->. ( ( th -> ps ) -> ( ph -> ( th -> ch ) ) ) ).
qed:6:	|- ( ( ph -> ( ps -> ch ) ) -> ( ( th -> ps ) -> ( ph -> ( th -> ch ) ) ) )

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

Assertion

Ref	Expression
syl5impVD	|- ( ( ph -> ( ps -> ch ) ) -> ( ( th -> ps ) -> ( ph -> ( th -> ch ) ) ) )

Proof of Theorem syl5impVD

Step	Hyp	Ref	Expression
1		idn2 38838	. . . . 5 |- (. ( ph -> ( ps -> ch ) ) ,. ( th -> ps ) ->. ( th -> ps ) ).
2		idn1 38790	. . . . . 6 |- (. ( ph -> ( ps -> ch ) ) ->. ( ph -> ( ps -> ch ) ) ).
3		pm2.04 90	. . . . . 6 |- ( ( ph -> ( ps -> ch ) ) -> ( ps -> ( ph -> ch ) ) )
4	2, 3	e1a 38852	. . . . 5 |- (. ( ph -> ( ps -> ch ) ) ->. ( ps -> ( ph -> ch ) ) ).
5		imim1 83	. . . . 5 |- ( ( th -> ps ) -> ( ( ps -> ( ph -> ch ) ) -> ( th -> ( ph -> ch ) ) ) )
6	1, 4, 5	e21 38957	. . . 4 |- (. ( ph -> ( ps -> ch ) ) ,. ( th -> ps ) ->. ( th -> ( ph -> ch ) ) ).
7		pm2.04 90	. . . 4 |- ( ( th -> ( ph -> ch ) ) -> ( ph -> ( th -> ch ) ) )
8	6, 7	e2 38856	. . 3 |- (. ( ph -> ( ps -> ch ) ) ,. ( th -> ps ) ->. ( ph -> ( th -> ch ) ) ).
9	8	in2 38830	. 2 |- (. ( ph -> ( ps -> ch ) ) ->. ( ( th -> ps ) -> ( ph -> ( th -> ch ) ) ) ).
10	9	in1 38787	1 |- ( ( ph -> ( ps -> ch ) ) -> ( ( th -> ps ) -> ( ph -> ( th -> ch ) ) ) )

Syntax hints:   -> wi 4

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

This theorem depends on definitions:  df-bi 197  df-an 386  df-vd1 38786  df-vd2 38794

This theorem is referenced by: (None)