Theorem pm11.7 41100

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 902	. 2 ⊢ ((𝜑 ∨ 𝜑) ↔ 𝜑)
2	1	2exbii 1850	1 ⊢ (∃𝑥∃𝑦(𝜑 ∨ 𝜑) ↔ ∃𝑥∃𝑦𝜑)

Syntax hints:   ↔ wb 209   ∨ wo 844  ∃wex 1781

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811

This theorem depends on definitions:  df-bi 210  df-or 845  df-ex 1782

This theorem is referenced by: (None)