Theorem 19.8w 1982

Description: Weak version of 19.8a 2174 and instance of 19.2d 1981. (Contributed by NM, 1-Aug-2017.) (Proof shortened by Wolf Lammen, 4-Dec-2017.) (Revised by BJ, 31-Mar-2021.)

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 1981	1 ⊢ (𝜑 → ∃𝑥𝜑)

Syntax hints:   → wi 4  ∀wal 1537  ∃wex 1782

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-6 1971

This theorem depends on definitions:  df-bi 206  df-ex 1783

This theorem is referenced by:  19.8v  1986  euae  2661  wl-moae  35675