Theorem exsimpr 1871

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 1837	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓)

Syntax hints:   → wi 4   ∧ wa 395  ∃wex 1781

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1782

This theorem is referenced by:  19.40  1888  elex2  2814  rexex  3068  ceqsexv2dOLD  3494  imassrn  6038  fv3  6860  elirrv  9514  finacn  9972  dfac4  10044  kmlem2  10074  ac6c5  10404  ac6s3  10409  ac6s5  10413  axnulALT2  35284  bj-finsumval0  37537  mptsnunlem  37590  topdifinffinlem  37599  heiborlem3  38061  ac6s3f  38419  moantr  38620