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Theorem eexinst11 28589
Description: exinst11 28703 without virtual deductions. (Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
eexinst11.1  |-  ( ph  ->  E. x ps )
eexinst11.2  |-  ( ph  ->  ( ps  ->  ch ) )
eexinst11.3  |-  ( ph  ->  A. x ph )
eexinst11.4  |-  ( ch 
->  A. x ch )
Assertion
Ref Expression
eexinst11  |-  ( ph  ->  ch )

Proof of Theorem eexinst11
StepHypRef Expression
1 eexinst11.1 . . 3  |-  ( ph  ->  E. x ps )
2 eexinst11.3 . . . 4  |-  ( ph  ->  A. x ph )
3 eexinst11.4 . . . 4  |-  ( ch 
->  A. x ch )
4 eexinst11.2 . . . 4  |-  ( ph  ->  ( ps  ->  ch ) )
52, 3, 4exlimdh 1816 . . 3  |-  ( ph  ->  ( E. x ps 
->  ch ) )
61, 5syl5com 26 . 2  |-  ( ph  ->  ( ph  ->  ch ) )
76pm2.43i 43 1  |-  ( ph  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1530   E.wex 1531
This theorem is referenced by:  vk15.4j  28590  exinst11  28703
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-nf 1535
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