Theorem pm4.24 399

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 395	1 ⊢ (𝜑 ↔ (𝜑 ∧ 𝜑))

This proof depends on syntax axioms:   ∧ wa 104   ↔ wb 105

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by:  anidm  400  anabsan  581  sbidm  1904  euind  3013  reuind  3031  xrmaxiflemcom  12017  rng1zrlem  14260  crngunit  14420  lmodvscl  14643