Metamath Proof Explorer
Description: /\ -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)
(New usage is discouraged.)
|
|
Ref |
Expression |
|
Hypotheses |
bnj835.1 |
⊢ ( 𝜂 ↔ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ) |
|
|
bnj835.2 |
⊢ ( 𝜑 → 𝜏 ) |
|
Assertion |
bnj835 |
⊢ ( 𝜂 → 𝜏 ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
bnj835.1 |
⊢ ( 𝜂 ↔ ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ) |
2 |
|
bnj835.2 |
⊢ ( 𝜑 → 𝜏 ) |
3 |
2
|
3ad2ant1 |
⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜏 ) |
4 |
1 3
|
sylbi |
⊢ ( 𝜂 → 𝜏 ) |