Theorem 19.2d 2004

Description: Deduction associated with 19.2 2003. (Contributed by BJ, 12-May-2019.)

Hypothesis

Ref	Expression
19.2d.1	⊢ (𝜑 → ∀𝑥𝜓)

Assertion

Ref	Expression
19.2d	⊢ (𝜑 → ∃𝑥𝜓)

Proof of Theorem 19.2d

Step	Hyp	Ref	Expression
1		19.2d.1	. 2 ⊢ (𝜑 → ∀𝑥𝜓)
2		19.2 2003	. 2 ⊢ (∀𝑥𝜓 → ∃𝑥𝜓)
3	1, 2	syl 18	1 ⊢ (𝜑 → ∃𝑥𝜓)

Syntax hints:   → wi 4  ∀wal 1565  ∃wex 1806

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-6 1994

This theorem depends on definitions:  df-bi 210  df-ex 1807

This theorem is referenced by:  19.8w  2005  nexmo  2575  aevdemo  30748  mh-regprimbi  36941