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  3491  imassrn  6026  fv3  6844  elirrv  9508  finacn  9963  dfac4  10035  kmlem2  10065  ac6c5  10395  ac6s3  10400  ac6s5  10404  axnulALT2  35062  bj-finsumval0  37261  mptsnunlem  37314  topdifinffinlem  37323  heiborlem3  37795  ac6s3f  38153  moantr  38334