This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 18-Feb-2008)
|
|
Ref |
Expression |
|
Hypothesis |
ad4ant3.1 |
⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 ) |
|
Assertion |
3adant3r3 |
⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜏 ) ) → 𝜃 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
ad4ant3.1 |
⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 ) |
| 2 |
1
|
3expb |
⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 ) |
| 3 |
2
|
3adantr3 |
⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜏 ) ) → 𝜃 ) |