Metamath Proof Explorer
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017) (Proof shortened by Wolf Lammen, 23-Jun-2022)
|
|
Ref |
Expression |
|
Hypothesis |
ad5ant.1 |
⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 ) |
|
Assertion |
ad5ant124 |
⊢ ( ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜏 ) ∧ 𝜒 ) ∧ 𝜂 ) → 𝜃 ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
ad5ant.1 |
⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 ) |
2 |
1
|
ad4ant124 |
⊢ ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜏 ) ∧ 𝜒 ) → 𝜃 ) |
3 |
2
|
adantr |
⊢ ( ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜏 ) ∧ 𝜒 ) ∧ 𝜂 ) → 𝜃 ) |