Theorem 19.37aiv 1900

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

Hypothesis

Ref	Expression
19.37aiv.1	⊢ ∃x(φ → ψ)

Assertion

Ref	Expression
19.37aiv	⊢ (φ → ∃xψ)

Distinct variable group:   φ,x

Allowed substitution hint:   ψ(x)

Proof of Theorem 19.37aiv

Step	Hyp	Ref	Expression
1		19.37aiv.1	. 2 ⊢ ∃x(φ → ψ)
2		19.37v 1899	. 2 ⊢ (∃x(φ → ψ) ↔ (φ → ∃xψ))
3	1, 2	mpbi 199	1 ⊢ (φ → ∃xψ)

This proof depends on syntax axioms:   → wi 4  ∃wex 1541

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

This theorem is used by:  eqvinc  2967