Theorem 19.40 1609

Description: Theorem 19.40 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
19.40	⊢ (∃x(φ ∧ ψ) → (∃xφ ∧ ∃xψ))

Proof of Theorem 19.40

Step	Hyp	Ref	Expression
1		exsimpl 1592	. 2 ⊢ (∃x(φ ∧ ψ) → ∃xφ)
2		simpr 447	. . 3 ⊢ ((φ ∧ ψ) → ψ)
3	2	eximi 1576	. 2 ⊢ (∃x(φ ∧ ψ) → ∃xψ)
4	1, 3	jca 518	1 ⊢ (∃x(φ ∧ ψ) → (∃xφ ∧ ∃xψ))

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:  19.40-2  1610  19.41  1879  exdistrf  1971  uniin  3912  copsexg  4608  dmin  4914  imadif  5172  fv3  5342