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Theorem eexinst01 28289
Description: exinst01 28397 without virtual deductions. (Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
eexinst01.1  |-  E. x ps
eexinst01.2  |-  ( ph  ->  ( ps  ->  ch ) )
eexinst01.3  |-  ( ph  ->  A. x ph )
eexinst01.4  |-  ( ch 
->  A. x ch )
Assertion
Ref Expression
eexinst01  |-  ( ph  ->  ch )

Proof of Theorem eexinst01
StepHypRef Expression
1 eexinst01.1 . 2  |-  E. x ps
2 eexinst01.3 . . 3  |-  ( ph  ->  A. x ph )
3 eexinst01.4 . . 3  |-  ( ch 
->  A. x ch )
4 eexinst01.2 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
52, 3, 4exlimdh 1804 . 2  |-  ( ph  ->  ( E. x ps 
->  ch ) )
61, 5mpi 16 1  |-  ( ph  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527   E.wex 1528
This theorem is referenced by:  vk15.4j  28291  exinst01  28397
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-nf 1532
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