Theorem 19.2 1570

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 1523	. 2 ⊢ (𝜑 → ∃𝑦𝜑)
2	1	sps 1471	1 ⊢ (∀𝑥𝜑 → ∃𝑦𝜑)

Syntax hints:   → wi 4  ∀wal 1283  ∃wex 1422

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  i19.24  1571  i19.39  1572  19.34  1615  eusv2i  4213