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Theorem syl5impVD 28955
Description: Virtual deduction proof of syl5imp 28573. 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,?: e1_ 28704  |-  (. ( ph  ->  ( ps  ->  ch ) )  ->.  ( ps  ->  ( ph  ->  ch ) ) ).
3::  |-  (. ( ph  ->  ( ps  ->  ch ) ) ,. ( th  ->  ps )  ->.  ( th  ->  ps ) ).
4:3,2,?: e21 28819  |-  (. ( ph  ->  ( ps  ->  ch ) ) ,. ( th  ->  ps )  ->.  ( th  ->  ( ph  ->  ch ) ) ).
5:4,?: e2 28708  |-  (. ( 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
StepHypRef Expression
1 idn2 28690 . . . . 5  |-  (. ( ph  ->  ( ps  ->  ch ) ) ,. ( th  ->  ps )  ->.  ( th  ->  ps ) ).
2 idn1 28641 . . . . . 6  |-  (. ( ph  ->  ( ps  ->  ch ) )  ->.  ( ph  ->  ( ps  ->  ch ) ) ).
3 pm2.04 76 . . . . . 6  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  ( ps  ->  ( ph  ->  ch ) ) )
42, 3e1_ 28704 . . . . 5  |-  (. ( ph  ->  ( ps  ->  ch ) )  ->.  ( ps  ->  ( ph  ->  ch ) ) ).
5 imim1 70 . . . . 5  |-  ( ( th  ->  ps )  ->  ( ( ps  ->  (
ph  ->  ch ) )  ->  ( th  ->  (
ph  ->  ch ) ) ) )
61, 4, 5e21 28819 . . . 4  |-  (. ( ph  ->  ( ps  ->  ch ) ) ,. ( th  ->  ps )  ->.  ( th  ->  ( ph  ->  ch ) ) ).
7 pm2.04 76 . . . 4  |-  ( ( th  ->  ( ph  ->  ch ) )  -> 
( ph  ->  ( th 
->  ch ) ) )
86, 7e2 28708 . . 3  |-  (. ( ph  ->  ( ps  ->  ch ) ) ,. ( th  ->  ps )  ->.  ( ph  ->  ( th  ->  ch ) ) ).
98in2 28682 . 2  |-  (. ( ph  ->  ( ps  ->  ch ) )  ->.  ( ( th  ->  ps )  -> 
( ph  ->  ( th 
->  ch ) ) ) ).
109in1 28638 1  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  (
( th  ->  ps )  ->  ( ph  ->  ( th  ->  ch )
) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-vd1 28637  df-vd2 28646
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