Theorem 19.33 1090

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 269	. . 3 ⊢ (φ → (φ ⋁ ψ))
2	1	19.20i 991	. 2 ⊢ (∀xφ → ∀x(φ ⋁ ψ))
3		olc 268	. . 3 ⊢ (ψ → (φ ⋁ ψ))
4	3	19.20i 991	. 2 ⊢ (∀xψ → ∀x(φ ⋁ ψ))
5	2, 4	jaoi 341	1 ⊢ ((∀xφ ⋁ ∀xψ) → ∀x(φ ⋁ ψ))

Syntax hints:   → wi 3   ⋁ wo 222  ∀wal 953

This theorem is referenced by:  19.33b 1091

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 962  ax-4 972  ax-5o 974

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225

Copyright terms: Public domain