This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem pm4.44

Description: Theorem *4.44 of WhiteheadRussell p. 119. (Contributed by NM, 3-Jan-2005)

Ref Expression
Assertion pm4.44 ( 𝜑 ↔ ( 𝜑 ∨ ( 𝜑 ∧ 𝜓 ) ) )

Proof

Step Hyp Ref Expression
1 orc ⊢ ( 𝜑 → ( 𝜑 ∨ ( 𝜑 ∧ 𝜓 ) ) )
2 id ⊢ ( 𝜑 → 𝜑 )
3 simpl ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜑 )
4 2 3 jaoi ⊢ ( ( 𝜑 ∨ ( 𝜑 ∧ 𝜓 ) ) → 𝜑 )
5 1 4 impbii ⊢ ( 𝜑 ↔ ( 𝜑 ∨ ( 𝜑 ∧ 𝜓 ) ) )