Theorem exsimpr 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
exsimpr	⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓)

Proof of Theorem exsimpr

Step	Hyp	Ref	Expression
1		simpr 484	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	eximi 1835	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓)

Syntax hints:   → wi 4   ∧ wa 395  ∃wex 1779

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780

This theorem is referenced by:  19.40  1886  elex2  2805  rexex  3059  ceqsexv2dOLD  3500  imassrn  6042  fv3  6876  finacn  10003  dfac4  10075  kmlem2  10105  ac6c5  10435  ac6s3  10440  ac6s5  10444  axnulALT2  35083  bj-finsumval0  37273  mptsnunlem  37326  topdifinffinlem  37335  heiborlem3  37807  ac6s3f  38165  moantr  38346