Theorem exsimpr 1896

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 489	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	eximi 1862	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓)

Syntax hints:   → wi 4   ∧ wa 400  ∃wex 1806

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836

This theorem depends on definitions:  df-bi 210  df-an 401  df-ex 1807

This theorem is referenced by:  19.40  1913  elex2  2846  rexex  3101  imassrn  6071  fv3  6897  elirrvOLD  9556  finacn  10030  dfac4  10102  kmlem2  10131  ac6c5  10462  ac6s3  10467  ac6s5  10471  axnulALT3  35440  bj-finsumval0  37812  mptsnunlem  37867  topdifinffinlem  37876  heiborlem3  38347  ac6s3f  38705  moantr  38906