Theorem 19.40 1906

Description: Theorem 19.40 of [Margaris] p. 90. (Contributed by NM, 26-May-1993.)

Assertion

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

Proof of Theorem 19.40

Step	Hyp	Ref	Expression
1		exsimpl 1888	. 2 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜑)
2		exsimpr 1889	. 2 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → ∃𝑥𝜓)
3	1, 2	jca 519	1 ⊢ (∃𝑥(𝜑 ∧ 𝜓) → (∃𝑥𝜑 ∧ ∃𝑥𝜓))

Syntax hints:   → wi 4   ∧ wa 399  ∃wex 1799

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1815  ax-4 1829

This theorem depends on definitions:  df-bi 209  df-an 400  df-ex 1800

This theorem is referenced by:  19.40-2  1907  19.40b  1908  19.41v  1969  19.41  2270  exdistrf  2478  uniinOLD  4890  copsexgwOLD  5459  copsexg  5460  dmin  5887  imadif  6605  oprabidw  7427  lfuhgr3  35470  bj-19.41al  37131  bj-nnfan  37229  bj-nnfand  37230  bj-19.42t  37240