Theorem 19.2g 2227

Description: Theorem 19.2 of [Margaris] p. 89, generalized to use two setvar variables. Use 19.2 2009 when sufficient. (Contributed by Mel L. O'Cat, 31-Mar-2008.)

Assertion

Ref	Expression
19.2g	⊢ (∀𝑥𝜑 → ∃𝑦𝜑)

Proof of Theorem 19.2g

Step	Hyp	Ref	Expression
1		19.8a 2220	. 2 ⊢ (𝜑 → ∃𝑦𝜑)
2	1	sps 2224	1 ⊢ (∀𝑥𝜑 → ∃𝑦𝜑)

This proof depends on syntax axioms:   → wi 4  ∀wal 1568  ∃wex 1812

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-12 2216

This proof depends on definitions:  df-bi 210  df-ex 1813

This theorem is used by: (None)