This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: Infer implication from a logical equivalence. Similar to biimpa .
(Contributed by NM, 4-Sep-2005)
|
|
Ref |
Expression |
|
Hypothesis |
biimp3a.1 |
⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 ↔ 𝜃 ) ) |
|
Assertion |
biimp3a |
⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
biimp3a.1 |
⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 ↔ 𝜃 ) ) |
| 2 |
1
|
biimpa |
⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 ) |
| 3 |
2
|
3impa |
⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 ) |