Theorem exsimpr 1864

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 483	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	eximi 1829	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓)

Syntax hints:   → wi 4   ∧ wa 394  ∃wex 1773

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803

This theorem depends on definitions:  df-bi 206  df-an 395  df-ex 1774

This theorem is referenced by:  19.40  1881  elex2  2807  rexex  3072  ceqsexv2d  3526  imassrn  6077  fv3  6918  finacn  10079  dfac4  10151  kmlem2  10180  ac6c5  10511  ac6s3  10516  ac6s5  10520  bj-finsumval0  36769  mptsnunlem  36822  topdifinffinlem  36831  heiborlem3  37291  ac6s3f  37649  moantr  37840