Theorem 19.37iv 1911

Description: Inference associated with 19.37v 1910. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
19.37iv.1	⊢ ∃𝑥(𝜑 → 𝜓)

Assertion

Ref	Expression
19.37iv	⊢ (𝜑 → ∃𝑥𝜓)

Distinct variable group:   𝜑,𝑥

Allowed substitution hint:   𝜓(𝑥)

Proof of Theorem 19.37iv

Step	Hyp	Ref	Expression
1		19.37iv.1	. 2 ⊢ ∃𝑥(𝜑 → 𝜓)
2		19.37v 1910	. 2 ⊢ (∃𝑥(𝜑 → 𝜓) ↔ (𝜑 → ∃𝑥𝜓))
3	1, 2	mpbi 220	1 ⊢ (𝜑 → ∃𝑥𝜓)

Syntax hints:   → wi 4  ∃wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888

This theorem depends on definitions:  df-bi 197  df-ex 1705

This theorem is referenced by:  bnd  8755  zfcndinf  9440  bnj1093  31048  bnj1186  31075  relopabVD  39137  elpglem2  42455