Theorem 19.33 1607

Description: Theorem 19.33 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.)

Assertion

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

Proof of Theorem 19.33

Step	Hyp	Ref	Expression
1		orc 374	. . 3 ⊢ (φ → (φ ∨ ψ))
2	1	alimi 1559	. 2 ⊢ (∀xφ → ∀x(φ ∨ ψ))
3		olc 373	. . 3 ⊢ (ψ → (φ ∨ ψ))
4	3	alimi 1559	. 2 ⊢ (∀xψ → ∀x(φ ∨ ψ))
5	2, 4	jaoi 368	1 ⊢ ((∀xφ ∨ ∀xψ) → ∀x(φ ∨ ψ))

This proof depends on syntax axioms:   → wi 4   ∨ wo 357  ∀wal 1540

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557

This proof depends on definitions:  df-bi 177  df-or 359

This theorem is used by:  19.33b  1608