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Metamath Proof Explorer
Description: Deduction adding 5 conjuncts to antecedent. (Contributed by Mario
Carneiro, 4-Jan-2017) (Proof shortened by Wolf Lammen, 5-Apr-2022)
|
|
Ref |
Expression |
|
Hypothesis |
ad2ant.1 |
⊢ ( 𝜑 → 𝜓 ) |
|
Assertion |
ad5antr |
⊢ ( ( ( ( ( ( 𝜑 ∧ 𝜒 ) ∧ 𝜃 ) ∧ 𝜏 ) ∧ 𝜂 ) ∧ 𝜁 ) → 𝜓 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
ad2ant.1 |
⊢ ( 𝜑 → 𝜓 ) |
| 2 |
1
|
adantr |
⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜓 ) |
| 3 |
2
|
ad4antr |
⊢ ( ( ( ( ( ( 𝜑 ∧ 𝜒 ) ∧ 𝜃 ) ∧ 𝜏 ) ∧ 𝜂 ) ∧ 𝜁 ) → 𝜓 ) |