Theorem 19.8w 2007

Description: Weak version of 19.8a 2216 and instance of 19.2d 2006. (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	1	19.2d 2006	1 ⊢ (𝜑 → ∃𝑥𝜑)

This proof depends on syntax axioms:   → wi 4  ∀wal 1567  ∃wex 1808

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-6 1996

This proof depends on definitions:  df-bi 210  df-ex 1809

This theorem is used by:  19.8v  2012  euae  2686  wl-moae  38199