Description: Deduction adding a conjunct to antecedent. (Contributed by Glauco Siliprandi, 11-Dec-2019)
Ref | Expression | ||
---|---|---|---|
Hypothesis | 3adantlr3.1 | ⊢ ( ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) ∧ 𝜃 ) → 𝜏 ) | |
Assertion | 3adantlr3 | ⊢ ( ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜂 ) ) ∧ 𝜃 ) → 𝜏 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3adantlr3.1 | ⊢ ( ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) ∧ 𝜃 ) → 𝜏 ) | |
2 | simpll | ⊢ ( ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜂 ) ) ∧ 𝜃 ) → 𝜑 ) | |
3 | simplr1 | ⊢ ( ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜂 ) ) ∧ 𝜃 ) → 𝜓 ) | |
4 | simplr2 | ⊢ ( ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜂 ) ) ∧ 𝜃 ) → 𝜒 ) | |
5 | 3 4 | jca | ⊢ ( ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜂 ) ) ∧ 𝜃 ) → ( 𝜓 ∧ 𝜒 ) ) |
6 | simpr | ⊢ ( ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜂 ) ) ∧ 𝜃 ) → 𝜃 ) | |
7 | 2 5 6 1 | syl21anc | ⊢ ( ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜂 ) ) ∧ 𝜃 ) → 𝜏 ) |