Theorem 19.33 770

Description: Theorem 19.33 of [Margaris] p. 90.

Assertion

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

Proof of Theorem 19.33

Step	Hyp	Ref	Expression
1		orc 225	. . 3 ⊢ (φ → (φ ∨ ψ))
2	1	19.20i 691	. 2 ⊢ (∀xφ → ∀x(φ ∨ ψ))
3		olc 224	. . 3 ⊢ (ψ → (φ ∨ ψ))
4	3	19.20i 691	. 2 ⊢ (∀xψ → ∀x(φ ∨ ψ))
5	2, 4	jaoi 275	1 ⊢ ((∀xφ ∨ ∀xψ) → ∀x(φ ∨ ψ))

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

This theorem is referenced by:  19.33b 771

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

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