Theorem 19.2g 2186

Description: Theorem 19.2 of [Margaris] p. 89, generalized to use two setvar variables. Use 19.2 1980 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 2179	. 2 ⊢ (𝜑 → ∃𝑦𝜑)
2	1	sps 2183	1 ⊢ (∀𝑥𝜑 → ∃𝑦𝜑)

Syntax hints:   → wi 4  ∀wal 1534  ∃wex 1779

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1969  ax-7 2014  ax-12 2176

This theorem depends on definitions:  df-bi 209  df-ex 1780

This theorem is referenced by: (None)