Theorem ad2antrr

Description: Deduction adding two conjuncts to antecedent. (Contributed by NM, 19-Oct-1999) (Proof shortened by Wolf Lammen, 20-Nov-2012)

	Ref	Expression
Hypothesis	ad2ant.1	⊢ ( 𝜑 → 𝜓 )
Assertion	ad2antrr	⊢ ( ( ( 𝜑 ∧ 𝜒 ) ∧ 𝜃 ) → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		ad2ant.1	⊢ ( 𝜑 → 𝜓 )
2	1	adantr	⊢ ( ( 𝜑 ∧ 𝜃 ) → 𝜓 )
3	2	adantlr	⊢ ( ( ( 𝜑 ∧ 𝜒 ) ∧ 𝜃 ) → 𝜓 )