Theorem pm4.24 390

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 386	1 ⊢ (𝜑 ↔ (𝜑 ∧ 𝜑))

Syntax hints:   ∧ wa 103   ↔ wb 104

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  anidm  391  anabsan  545  sbidm  1790  euind  2824  reuind  2842  xrmaxiflemcom  10857