Metamath Proof Explorer
Description: 3impib with the implications of the hypothesis biconditionals.
(Contributed by Alan Sare, 6-Nov-2017)
|
|
Ref |
Expression |
|
Hypothesis |
bi123impib.1 |
⊢ ( 𝜑 ↔ ( ( 𝜓 ∧ 𝜒 ) ↔ 𝜃 ) ) |
|
Assertion |
bi123impib |
⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
bi123impib.1 |
⊢ ( 𝜑 ↔ ( ( 𝜓 ∧ 𝜒 ) ↔ 𝜃 ) ) |
2 |
1
|
biimpi |
⊢ ( 𝜑 → ( ( 𝜓 ∧ 𝜒 ) ↔ 𝜃 ) ) |
3 |
2
|
bi23impib |
⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 ) |