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Metamath Proof Explorer
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017) (Proof shortened by Wolf Lammen, 14-Apr-2022)
|
|
Ref |
Expression |
|
Hypothesis |
ad4ant2.1 |
⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) |
|
Assertion |
ad4ant13 |
⊢ ( ( ( ( 𝜑 ∧ 𝜃 ) ∧ 𝜓 ) ∧ 𝜏 ) → 𝜒 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
ad4ant2.1 |
⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) |
| 2 |
1
|
adantr |
⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜏 ) → 𝜒 ) |
| 3 |
2
|
adantllr |
⊢ ( ( ( ( 𝜑 ∧ 𝜃 ) ∧ 𝜓 ) ∧ 𝜏 ) → 𝜒 ) |