Theorem 19.2 1618

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 1570	. 2 ⊢ (𝜑 → ∃𝑦𝜑)
2	1	sps 1518	1 ⊢ (∀𝑥𝜑 → ∃𝑦𝜑)

Syntax hints:   → wi 4  ∀wal 1330  ∃wex 1469

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1488

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  i19.24  1619  i19.39  1620  19.34  1663  eusv2i  4384