Theorem pm4.24 375

Description: Theorem *4.24 of [WhiteheadRussell] p. 117. (Contributed by NM, 3-Jan-2005.) (Revised by NM, 14-Mar-2014.)

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 371	1 ⊢ (φ ↔ (φ ∧ φ))

Syntax hints:   ∧ wa 97   ↔ wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  anidm  376  anabsan  509  sbidm  1728  euind  2722  reuind  2738