Theorem 19.35i 1513

Description: Inference from Theorem 19.35 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 2-Feb-2015.)

Hypothesis

Ref	Expression
19.35i.1	⊢ ∃x(φ → ψ)

Assertion

Ref	Expression
19.35i	⊢ (∀xφ → ∃xψ)

Proof of Theorem 19.35i

Step	Hyp	Ref	Expression
1		19.35i.1	. 2 ⊢ ∃x(φ → ψ)
2		19.35-1 1512	. 2 ⊢ (∃x(φ → ψ) → (∀xφ → ∃xψ))
3	1, 2	ax-mp 7	1 ⊢ (∀xφ → ∃xψ)

Syntax hints:   → wi 4  ∀wal 1240  ∃wex 1378

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-ial 1424

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  19.36i  1559  spimed  1625