Theorem pm11.7 44415

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 905	. 2 ⊢ ((𝜑 ∨ 𝜑) ↔ 𝜑)
2	1	2exbii 1849	1 ⊢ (∃𝑥∃𝑦(𝜑 ∨ 𝜑) ↔ ∃𝑥∃𝑦𝜑)

Syntax hints:   ↔ wb 206   ∨ wo 848  ∃wex 1779

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809

This theorem depends on definitions:  df-bi 207  df-or 849  df-ex 1780

This theorem is referenced by: (None)