Theorem 19.2g 1757

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

Assertion

Ref	Expression
19.2g	⊢ (∀xφ → ∃yφ)

Proof of Theorem 19.2g

Step	Hyp	Ref	Expression
1		19.8a 1756	. 2 ⊢ (φ → ∃yφ)
2	1	sps 1754	1 ⊢ (∀xφ → ∃yφ)

Syntax hints:   → wi 4  ∀wal 1540  ∃wex 1541

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542

This theorem is referenced by: (None)