Theorem 19.8w 1660

Description: Weak version of 19.8a 1756. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 1-Aug-2017.) (Proof shortened by Wolf Lammen, 4-Dec-2017.)

Hypothesis

Ref	Expression
19.8w.1	⊢ (φ → ∀xφ)

Assertion

Ref	Expression
19.8w	⊢ (φ → ∃xφ)

Proof of Theorem 19.8w

Step	Hyp	Ref	Expression
1		19.8w.1	. 2 ⊢ (φ → ∀xφ)
2		19.2 1659	. 2 ⊢ (∀xφ → ∃xφ)
3	1, 2	syl 15	1 ⊢ (φ → ∃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:  19.9v  1664