Theorem pm11.7 41903

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 901	. 2 ⊢ ((𝜑 ∨ 𝜑) ↔ 𝜑)
2	1	2exbii 1852	1 ⊢ (∃𝑥∃𝑦(𝜑 ∨ 𝜑) ↔ ∃𝑥∃𝑦𝜑)

Syntax hints:   ↔ wb 205   ∨ wo 843  ∃wex 1783

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813

This theorem depends on definitions:  df-bi 206  df-or 844  df-ex 1784

This theorem is referenced by: (None)