Theorem pm11.7 45379

Description: Theorem *11.7 in [WhiteheadRussell] p. 166. (Contributed by Andrew Salmon, 24-May-2011.)

Assertion

Ref	Expression
pm11.7	⊢ (∃𝑥∃𝑦(𝜑 ∨ 𝜑) ↔ ∃𝑥∃𝑦𝜑)

Proof of Theorem pm11.7

Step	Hyp	Ref	Expression
1		oridm 918	. 2 ⊢ ((𝜑 ∨ 𝜑) ↔ 𝜑)
2	1	2exbii 1882	1 ⊢ (∃𝑥∃𝑦(𝜑 ∨ 𝜑) ↔ ∃𝑥∃𝑦𝜑)

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)