Theorem 19.35i 1601

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

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 1600	. 2 ⊢ (∃x(φ → ψ) ↔ (∀xφ → ∃xψ))
3	1, 2	mpbi 199	1 ⊢ (∀xφ → ∃xψ)

Syntax hints:   → wi 4  ∀wal 1540  ∃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:  19.2  1659  spimeh  1667  cbv3hv  1850