Metamath Proof Explorer
Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 27-Dec-2007)
|
|
Ref |
Expression |
|
Hypothesis |
3ad2antl.1 |
⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 ) |
|
Assertion |
3ad2antr2 |
⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜏 ) ) → 𝜃 ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
3ad2antl.1 |
⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 ) |
2 |
1
|
adantrl |
⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 ) |
3 |
2
|
3adantr3 |
⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜏 ) ) → 𝜃 ) |