Theorem exsimpr 1671

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 110	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
2	1	eximi 1653	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓)

This proof depends on syntax axioms:   → wi 4   ∧ wa 104  ∃wex 1545

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-4 1563  ax-ial 1587

This proof depends on definitions:  df-bi 117

This theorem is used by:  cbvexv1  1805  onm  4546  imassrn  5137  eliotaeu  5366  fv3  5718  relelfvdm  5727  nfvres  5732  brtpos2  6522  finacn  7560  cc1  7631  acnccim  7638  omiunct  13335