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Theorem exsimpl 1835
Description: Simplification of an existentially quantified conjunction. (Contributed by Rodolfo Medina, 25-Sep-2010.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
exsimpl (∃𝑥(𝜑𝜓) → ∃𝑥𝜑)

Proof of Theorem exsimpl
StepHypRef Expression
1 simpl 472 . 2 ((𝜑𝜓) → 𝜑)
21eximi 1802 1 (∃𝑥(𝜑𝜓) → ∃𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  wex 1744
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1745
This theorem is referenced by:  19.40  1837  euexALT  2540  moexex  2570  elex  3243  sbc5  3493  r19.2zb  4094  dmcoss  5417  suppimacnvss  7350  unblem2  8254  kmlem8  9017  isssc  16527  bnj1143  30987  bnj1371  31223  bnj1374  31225  bj-elissetv  32986  atex  35010  rtrclex  38241  clcnvlem  38247  pm10.55  38885
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