Theorem 19.37v 1899

Description: Special case of Theorem 19.37 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
19.37v	⊢ (∃x(φ → ψ) ↔ (φ → ∃xψ))

Distinct variable group:   φ,x

Allowed substitution hint:   ψ(x)

Proof of Theorem 19.37v

Step	Hyp	Ref	Expression
1		nfv 1619	. 2 ⊢ Ⅎxφ
2	1	19.37 1873	1 ⊢ (∃x(φ → ψ) ↔ (φ → ∃xψ))

Syntax hints:   → wi 4   ↔ wb 176  ∃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-an 360  df-ex 1542  df-nf 1545

This theorem is referenced by:  19.37aiv  1900  moanim  2260