Theorem pm4.24 624

Description: Theorem *4.24 of [WhiteheadRussell] p. 117. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.24	⊢ (φ ↔ (φ ∧ φ))

Proof of Theorem pm4.24

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ (φ → φ)
2	1	pm4.71i 613	1 ⊢ (φ ↔ (φ ∧ φ))

Syntax hints:   ↔ wb 176   ∧ wa 358

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

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  anidm  625  anabsan  786  nic-ax  1438  euind  3024  reuind  3040