Theorem 19.34 772

Description: Theorem 19.34 of [Margaris] p. 90.

Assertion

Ref	Expression
19.34	⊢ ((∀xφ ∨ ∃xψ) → ∃x(φ ∨ ψ))

Proof of Theorem 19.34

Step	Hyp	Ref	Expression
1		19.2 713	. . 3 ⊢ (∀xφ → ∃xφ)
2	1	orim1i 272	. 2 ⊢ ((∀xφ ∨ ∃xψ) → (∃xφ ∨ ∃xψ))
3		19.43 767	. 2 ⊢ (∃x(φ ∨ ψ) ↔ (∃xφ ∨ ∃xψ))
4	2, 3	sylibr 175	1 ⊢ ((∀xφ ∨ ∃xψ) → ∃x(φ ∨ ψ))

Syntax hints:   → wi 2   ∨ wo 195  ∀wal 672  ∃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

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679

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