Theorem pm10.42 45115

Description: Theorem *10.42 in [WhiteheadRussell] p. 155. (Contributed by Andrew Salmon, 17-Jun-2011.)

Assertion

Ref	Expression
pm10.42	⊢ ((∃𝑥𝜑 ∨ ∃𝑥𝜓) ↔ ∃𝑥(𝜑 ∨ 𝜓))

Proof of Theorem pm10.42

Step	Hyp	Ref	Expression
1		19.43 1915	. 2 ⊢ (∃𝑥(𝜑 ∨ 𝜓) ↔ (∃𝑥𝜑 ∨ ∃𝑥𝜓))
2	1	bicomi 227	1 ⊢ ((∃𝑥𝜑 ∨ ∃𝑥𝜓) ↔ ∃𝑥(𝜑 ∨ 𝜓))

This proof depends on syntax axioms:   ↔ wb 209   ∨ wo 861  ∃wex 1812

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842

This proof depends on definitions:  df-bi 210  df-or 862  df-ex 1813

This theorem is used by: (None)