This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: Theorem *5.44 of WhiteheadRussell p. 125. (Contributed by NM, 3-Jan-2005)
|
|
Ref |
Expression |
|
Assertion |
pm5.44 |
⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜑 → 𝜒 ) ↔ ( 𝜑 → ( 𝜓 ∧ 𝜒 ) ) ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
jcab |
⊢ ( ( 𝜑 → ( 𝜓 ∧ 𝜒 ) ) ↔ ( ( 𝜑 → 𝜓 ) ∧ ( 𝜑 → 𝜒 ) ) ) |
| 2 |
1
|
baibr |
⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜑 → 𝜒 ) ↔ ( 𝜑 → ( 𝜓 ∧ 𝜒 ) ) ) ) |