Theorem adantl4r

Description: Deduction adding 1 conjunct to antecedent. (Contributed by Thierry Arnoux, 11-Feb-2018)

	Ref	Expression
Hypothesis	adantl4r.1	⊢ ( ( ( ( ( 𝜑 ∧ 𝜎 ) ∧ 𝜌 ) ∧ 𝜇 ) ∧ 𝜆 ) → 𝜅 )
Assertion	adantl4r	⊢ ( ( ( ( ( ( 𝜑 ∧ 𝜁 ) ∧ 𝜎 ) ∧ 𝜌 ) ∧ 𝜇 ) ∧ 𝜆 ) → 𝜅 )

Proof

Step	Hyp	Ref	Expression
1		adantl4r.1	⊢ ( ( ( ( ( 𝜑 ∧ 𝜎 ) ∧ 𝜌 ) ∧ 𝜇 ) ∧ 𝜆 ) → 𝜅 )
2	1	ex	⊢ ( ( ( ( 𝜑 ∧ 𝜎 ) ∧ 𝜌 ) ∧ 𝜇 ) → ( 𝜆 → 𝜅 ) )
3	2	adantl3r	⊢ ( ( ( ( ( 𝜑 ∧ 𝜁 ) ∧ 𝜎 ) ∧ 𝜌 ) ∧ 𝜇 ) → ( 𝜆 → 𝜅 ) )
4	3	imp	⊢ ( ( ( ( ( ( 𝜑 ∧ 𝜁 ) ∧ 𝜎 ) ∧ 𝜌 ) ∧ 𝜇 ) ∧ 𝜆 ) → 𝜅 )