Theorem exsimpr 1870

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 1836	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓)

Syntax hints:   → wi 4   ∧ wa 395  ∃wex 1780

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1781

This theorem is referenced by:  19.40  1887  elex2  2813  rexex  3066  ceqsexv2dOLD  3492  imassrn  6030  fv3  6852  elirrv  9502  finacn  9960  dfac4  10032  kmlem2  10062  ac6c5  10392  ac6s3  10397  ac6s5  10401  axnulALT2  35265  bj-finsumval0  37490  mptsnunlem  37543  topdifinffinlem  37552  heiborlem3  38014  ac6s3f  38372  moantr  38557