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Theorem exsimpl 1792
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 473 . 2 ((𝜑𝜓) → 𝜑)
21eximi 1759 1 (∃𝑥(𝜑𝜓) → ∃𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  wex 1701
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734
This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1702
This theorem is referenced by:  19.40  1794  euexALT  2510  moexex  2540  elex  3198  sbc5  3442  r19.2zb  4033  dmcoss  5345  suppimacnvss  7250  unblem2  8157  kmlem8  8923  isssc  16401  bnj1143  30566  bnj1371  30802  bnj1374  30804  bj-elissetv  32505  atex  34169  rtrclex  37402  clcnvlem  37408  pm10.55  38047
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