Theorem 19.39 761

Description: Theorem 19.39 of [Margaris] p. 90.

Assertion

Ref	Expression
19.39	⊢ ((∃xφ → ∃xψ) → ∃x(φ → ψ))

Proof of Theorem 19.39

Step	Hyp	Ref	Expression
1		19.2 713	. . 3 ⊢ (∀xφ → ∃xφ)
2	1	syl4 19	. 2 ⊢ ((∃xφ → ∃xψ) → (∀xφ → ∃xψ))
3		19.35 754	. 2 ⊢ (∃x(φ → ψ) ↔ (∀xφ → ∃xψ))
4	2, 3	sylibr 175	1 ⊢ ((∃xφ → ∃xψ) → ∃x(φ → ψ))

Syntax hints:   → wi 2  ∀wal 672  ∃wex 678

This theorem is referenced by:  iununi 2037

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

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

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