Metamath Proof Explorer
Description: Similar to 3impa with implication in hypothesis replaced by
biconditional. (Contributed by Alan Sare, 6-Nov-2017)
|
|
Ref |
Expression |
|
Hypothesis |
bi3impa.1 |
⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ↔ 𝜃 ) |
|
Assertion |
bi3impa |
⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
bi3impa.1 |
⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ↔ 𝜃 ) |
2 |
1
|
biimpi |
⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 ) |
3 |
2
|
3impa |
⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 ) |