Description: Deduction adding a conjunct to antecedent. (Contributed by Glauco Siliprandi, 11-Dec-2019)
Ref | Expression | ||
---|---|---|---|
Hypothesis | 3adantll3.1 | ⊢ ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 ) | |
Assertion | 3adantll3 | ⊢ ( ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜂 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3adantll3.1 | ⊢ ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 ) | |
2 | simpll1 | ⊢ ( ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜂 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜑 ) | |
3 | simpll2 | ⊢ ( ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜂 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜓 ) | |
4 | 2 3 | jca | ⊢ ( ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜂 ) ∧ 𝜒 ) ∧ 𝜃 ) → ( 𝜑 ∧ 𝜓 ) ) |
5 | simplr | ⊢ ( ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜂 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜒 ) | |
6 | simpr | ⊢ ( ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜂 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜃 ) | |
7 | 4 5 6 1 | syl21anc | ⊢ ( ( ( ( 𝜑 ∧ 𝜓 ∧ 𝜂 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 ) |