Theorem exsimpr 1888

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
exsimpr	⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓)

Proof of Theorem exsimpr

Step	Hyp	Ref	Expression
1		simpr 488	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	eximi 1854	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓)

Syntax hints:   → wi 4   ∧ wa 399  ∃wex 1798

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828

This theorem depends on definitions:  df-bi 209  df-an 400  df-ex 1799

This theorem is referenced by:  19.40  1905  elex2  2838  rexex  3091  imassrn  6056  fv3  6880  elirrvOLD  9540  finacn  10000  dfac4  10072  kmlem2  10102  ac6c5  10433  ac6s3  10438  ac6s5  10442  axnulALT3  35365  bj-finsumval0  37738  mptsnunlem  37793  topdifinffinlem  37802  heiborlem3  38273  ac6s3f  38631  moantr  38832