This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007)
|
|
Ref |
Expression |
|
Hypothesis |
3ad2antl.1 |
⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 ) |
|
Assertion |
3ad2antl1 |
⊢ ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜏 ) ∧ 𝜒 ) → 𝜃 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
3ad2antl.1 |
⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 ) |
| 2 |
1
|
adantlr |
⊢ ( ( ( 𝜑 ∧ 𝜏 ) ∧ 𝜒 ) → 𝜃 ) |
| 3 |
2
|
3adantl2 |
⊢ ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜏 ) ∧ 𝜒 ) → 𝜃 ) |