This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: Deduce an implication from a logical equivalence. Deduction associated
with biimp and biimpi . (Contributed by NM, 11-Jan-1993)
|
|
Ref |
Expression |
|
Hypothesis |
biimpd.1 |
⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) |
|
Assertion |
biimpd |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
biimpd.1 |
⊢ ( 𝜑 → ( 𝜓 ↔ 𝜒 ) ) |
| 2 |
|
biimp |
⊢ ( ( 𝜓 ↔ 𝜒 ) → ( 𝜓 → 𝜒 ) ) |
| 3 |
1 2
|
syl |
⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) ) |