Theorem ad3antlr

Description: Deduction adding three conjuncts to antecedent. (Contributed by Mario Carneiro, 5-Jan-2017) (Proof shortened by Wolf Lammen, 5-Apr-2022)

	Ref	Expression
Hypothesis	ad2ant.1	⊢ ( 𝜑 → 𝜓 )
Assertion	ad3antlr	⊢ ( ( ( ( 𝜒 ∧ 𝜑 ) ∧ 𝜃 ) ∧ 𝜏 ) → 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		ad2ant.1	⊢ ( 𝜑 → 𝜓 )
2	1	adantl	⊢ ( ( 𝜒 ∧ 𝜑 ) → 𝜓 )
3	2	ad2antrr	⊢ ( ( ( ( 𝜒 ∧ 𝜑 ) ∧ 𝜃 ) ∧ 𝜏 ) → 𝜓 )