Theorem exsimpr 1868

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 1833	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓)

Syntax hints:   → wi 4   ∧ wa 395  ∃wex 1777

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1778

This theorem is referenced by:  19.40  1885  elex2  2821  rexex  3082  ceqsexv2dOLD  3546  imassrn  6100  fv3  6938  finacn  10119  dfac4  10191  kmlem2  10221  ac6c5  10551  ac6s3  10556  ac6s5  10560  axnulALT2  35069  bj-finsumval0  37251  mptsnunlem  37304  topdifinffinlem  37313  heiborlem3  37773  ac6s3f  38131  moantr  38320