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Theorem exsimpl 1944
 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 474 . 2 ((𝜑𝜓) → 𝜑)
21eximi 1911 1 (∃𝑥(𝜑𝜓) → ∃𝑥𝜑)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383  ∃wex 1853 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886 This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1854 This theorem is referenced by:  19.40  1946  euexALT  2649  moexex  2679  elex  3352  sbc5  3601  r19.2zb  4205  dmcoss  5540  suppimacnvss  7474  unblem2  8380  kmlem8  9191  isssc  16701  bnj1143  31189  bnj1371  31425  bnj1374  31427  bj-elissetv  33183  atex  35213  rtrclex  38444  clcnvlem  38450  pm10.55  39088
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