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Metamath Proof Explorer
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 16-Jul-1995) (Proof shortened by Wolf Lammen, 21-Jun-2022)
|
|
Ref |
Expression |
|
Hypothesis |
3adant.1 |
⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) |
|
Assertion |
3adant3 |
⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜃 ) → 𝜒 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
3adant.1 |
⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) |
| 2 |
1
|
adantrr |
⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜃 ) ) → 𝜒 ) |
| 3 |
2
|
3impb |
⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜃 ) → 𝜒 ) |