Theorem exsimpr 1833

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 477	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	eximi 1798	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓)

Syntax hints:   → wi 4   ∧ wa 387  ∃wex 1743

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1759  ax-4 1773

This theorem depends on definitions:  df-bi 199  df-an 388  df-ex 1744

This theorem is referenced by:  19.40  1850  spsbeOLDOLD  2432  spsbeALT  2517  rexex  3180  ceqsexv2d  3456  imassrn  5778  fv3  6514  finacn  9268  dfac4  9340  kmlem2  9369  ac6c5  9700  ac6s3  9705  ac6s5  9709  bj-finsumval0  34067  mptsnunlem  34098  topdifinffinlem  34107  heiborlem3  34570  ac6s3f  34930  moantr  35099