Theorem 19.36v 1896

Description: Special case of Theorem 19.36 of [Margaris] p. 90. (Contributed by NM, 18-Aug-1993.)

Assertion

Ref	Expression
19.36v	⊢ (∃x(φ → ψ) ↔ (∀xφ → ψ))

Distinct variable group:   ψ,x

Allowed substitution hint:   φ(x)

Proof of Theorem 19.36v

Step	Hyp	Ref	Expression
1		nfv 1619	. 2 ⊢ Ⅎxψ
2	1	19.36 1871	1 ⊢ (∃x(φ → ψ) ↔ (∀xφ → ψ))

Syntax hints:   → wi 4   ↔ wb 176  ∀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-6 1729  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545

This theorem is referenced by:  19.12vv  1898  axext2  2335  vtocl2  2911  vtocl3  2912