Theorem exsimpl 1592

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
exsimpl	⊢ (∃x(φ ∧ ψ) → ∃xφ)

Proof of Theorem exsimpl

Step	Hyp	Ref	Expression
1		simpl 443	. 2 ⊢ ((φ ∧ ψ) → φ)
2	1	eximi 1576	1 ⊢ (∃x(φ ∧ ψ) → ∃xφ)

Syntax hints:   → wi 4   ∧ wa 358  ∃wex 1541

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557

This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542

This theorem is referenced by:  19.40  1609  euex  2227  moexex  2273  elex  2868  sbc5  3071  r19.2zb  3641