Theorem exsimpr 1867

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 1832	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓)

Syntax hints:   → wi 4   ∧ wa 395  ∃wex 1776

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1777

This theorem is referenced by:  19.40  1884  elex2  2816  rexex  3074  ceqsexv2dOLD  3534  imassrn  6091  fv3  6925  finacn  10088  dfac4  10160  kmlem2  10190  ac6c5  10520  ac6s3  10525  ac6s5  10529  axnulALT2  35086  bj-finsumval0  37268  mptsnunlem  37321  topdifinffinlem  37330  heiborlem3  37800  ac6s3f  38158  moantr  38346