Theorem exsimpr 1796

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 1762	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓)

Syntax hints:   → wi 4   ∧ wa 384  ∃wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705

This theorem is referenced by:  19.40  1797  spsbe  1884  rexex  3002  ceqsexv2d  3243  imassrn  5477  fv3  6206  finacn  8873  dfac4  8945  kmlem2  8973  ac6c5  9304  ac6s3  9309  ac6s5  9313  bj-finsumval0  33147  mptsnunlem  33185  topdifinffinlem  33195  heiborlem3  33612  ac6s3f  33979  motr  34127