Theorem 3adantlr3

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 )

Proof

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 )