Theorem exinst 37870

Description: Existential Instantiation. Virtual deduction form of exlimexi 37751. (Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
exinst.1	⊢ (𝜓 → ∀𝑥𝜓)
exinst.2	⊢ (   ∃𝑥𝜑   ,   𝜑   ▶   𝜓   )

Assertion

Ref	Expression
exinst	⊢ (∃𝑥𝜑 → 𝜓)

Proof of Theorem exinst

Step	Hyp	Ref	Expression
1		exinst.1	. 2 ⊢ (𝜓 → ∀𝑥𝜓)
2		exinst.2	. . 3 ⊢ (   ∃𝑥𝜑   ,   𝜑   ▶   𝜓   )
3	2	dfvd2i 37822	. 2 ⊢ (∃𝑥𝜑 → (𝜑 → 𝜓))
4	1, 3	exlimexi 37751	1 ⊢ (∃𝑥𝜑 → 𝜓)

Syntax hints:   → wi 4  ∀wal 1473  ∃wex 1695  (   wvd2 37814

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-12 2034

This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696  df-nf 1701  df-vd2 37815

This theorem is referenced by:  sb5ALTVD  38171