Theorem 19.2 1529

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

Assertion

Ref	Expression
19.2	⊢ (∀𝑥𝜑 → ∃𝑦𝜑)

Proof of Theorem 19.2

Step	Hyp	Ref	Expression
1		19.8a 1482	. 2 ⊢ (𝜑 → ∃𝑦𝜑)
2	1	sps 1430	1 ⊢ (∀𝑥𝜑 → ∃𝑦𝜑)

Syntax hints:   → wi 4  ∀wal 1241  ∃wex 1381

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  i19.24  1530  i19.39  1531  19.34  1574  eusv2i  4187