This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: Theorem *5.3 of WhiteheadRussell p. 125. (Contributed by NM, 3-Jan-2005) (Proof shortened by Andrew Salmon, 7-May-2011)
|
|
Ref |
Expression |
|
Assertion |
pm5.3 |
⊢ ( ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) ↔ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜑 ∧ 𝜒 ) ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
simpl |
⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜑 ) |
| 2 |
1
|
biantrurd |
⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 ↔ ( 𝜑 ∧ 𝜒 ) ) ) |
| 3 |
2
|
pm5.74i |
⊢ ( ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) ↔ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜑 ∧ 𝜒 ) ) ) |