Theorem 19.2 1659

Description: Theorem 19.2 of [Margaris] p. 89. Note: This proof is very different from Margaris' because we only have Tarski's FOL axiom schemes available at this point. See the later 19.2g 1757 for a more conventional proof. (Contributed by NM, 2-Aug-2017.) (Revised by Wolf Lammen to remove dependency on ax-8, 4-Dec-2017.)

Assertion

Ref	Expression
19.2	⊢ (∀xφ → ∃xφ)

Proof of Theorem 19.2

Step	Hyp	Ref	Expression
1		id 19	. . 3 ⊢ (φ → φ)
2	1	exiftru 1657	. 2 ⊢ ∃x(φ → φ)
3	2	19.35i 1601	1 ⊢ (∀xφ → ∃xφ)

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  ax-9 1654

This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542

This theorem is referenced by:  19.8w  1660  19.39  1661  19.24  1662  19.34  1663