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Theorem exsimpl 1869
 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 486 . 2 ((𝜑𝜓) → 𝜑)
21eximi 1836 1 (∃𝑥(𝜑𝜓) → ∃𝑥𝜑)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 399  ∃wex 1781 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782 This theorem is referenced by:  19.40  1887  moexexlem  2688  elisset  3452  elex  3459  sbc5  3748  r19.2zb  4399  dmcoss  5807  suppimacnvss  7823  unblem2  8755  kmlem8  9568  isssc  17082  krull  31051  bnj1143  32172  bnj1371  32411  bnj1374  32413  bj-elissetv  34315  atex  36702  rtrclex  40315  clcnvlem  40321  pm10.55  41071
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