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Theorem al2imi 1606
Description: Inference quantifying antecedent, nested antecedent, and consequent. (Contributed by NM, 10-Jan-1993.)
Hypothesis
Ref Expression
al2imi.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
al2imi  |-  ( A. x ph  ->  ( A. x ps  ->  A. x ch ) )

Proof of Theorem al2imi
StepHypRef Expression
1 al2imi.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
21alimi 1604 . 2  |-  ( A. x ph  ->  A. x
( ps  ->  ch ) )
3 alim 1603 . 2  |-  ( A. x ( ps  ->  ch )  ->  ( A. x ps  ->  A. x ch ) )
42, 3syl 16 1  |-  ( A. x ph  ->  ( A. x ps  ->  A. x ch ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1367
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1591  ax-4 1602
This theorem is referenced by:  alanimi  1607  alimdh  1608  albi  1609  aleximi  1622  eximOLD  1624  19.33b  1663  axc112  1870  axc10  1948  cbv1hOLD  1963  axc11nlem  1996  equveliOLD  2039  sbequi  2066  sbi1  2084  sbal1OLD  2172  axc11-o  2252  moim  2319  2eu6  2370  ralim  2785  ceqsalt  2993  difin0ss  3743  intss  4147  hbntg  27617  wl-aetr  28356  wl-aleq  28361  wl-nfeqfb  28363  pm10.57  29620  2al2imi  29622  19.41rg  31256  hbntal  31259  bj-2alim  32140  bj-axc10v  32210  bj-axc11nlemv  32247  bj-ceqsalt0  32381  bj-ceqsalt1  32382
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