Theorem 3adant3r2

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 17-Feb-2008)

	Ref	Expression
Hypothesis	ad4ant3.1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
Assertion	3adant3r2	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜏 ∧ 𝜒 ) ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		ad4ant3.1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
2	1	3expb	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ) ) → 𝜃 )
3	2	3adantr2	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜏 ∧ 𝜒 ) ) → 𝜃 )