Theorem 19.37aiv 962

Description: Inference from Theorem 19.37 of [Margaris] p. 90.

Hypothesis

Ref	Expression
19.37aiv.1	⊢ ∃x(φ → ψ)

Assertion

Ref	Expression
19.37aiv	⊢ (φ → ∃xψ)

Distinct variable group(s):   φ,x

Proof of Theorem 19.37aiv

Step	Hyp	Ref	Expression
1		19.37aiv.1	. 2 ⊢ ∃x(φ → ψ)
2		19.37v 961	. 2 ⊢ (∃x(φ → ψ) ↔ (φ → ∃xψ))
3	1, 2	mpbi 164	1 ⊢ (φ → ∃xψ)

Syntax hints:   → wi 2  ∃wex 678

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-gen 677  ax-17 925

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679

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