Theorem 19.34 1990

Description: Theorem 19.34 of [Margaris] p. 90. (Contributed by NM, 12-Mar-1993.)

Assertion

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

Proof of Theorem 19.34

Step	Hyp	Ref	Expression
1		19.2 1980	. . 3 ⊢ (∀𝑥𝜑 → ∃𝑥𝜑)
2	1	orim1i 907	. 2 ⊢ ((∀𝑥𝜑 ∨ ∃𝑥𝜓) → (∃𝑥𝜑 ∨ ∃𝑥𝜓))
3		19.43 1885	. 2 ⊢ (∃𝑥(𝜑 ∨ 𝜓) ↔ (∃𝑥𝜑 ∨ ∃𝑥𝜓))
4	2, 3	sylibr 233	1 ⊢ ((∀𝑥𝜑 ∨ ∃𝑥𝜓) → ∃𝑥(𝜑 ∨ 𝜓))

Syntax hints:   → wi 4   ∨ wo 844  ∀wal 1537  ∃wex 1782

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-6 1971

This theorem depends on definitions:  df-bi 206  df-or 845  df-ex 1783

This theorem is referenced by: (None)