Theorem ad5ant2345

Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017)

	Ref	Expression
Hypothesis	ad5ant2345.1	⊢ ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 )
Assertion	ad5ant2345	⊢ ( ( ( ( ( 𝜂 ∧ 𝜑 ) ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 )

Proof

Step	Hyp	Ref	Expression
1		ad5ant2345.1	⊢ ( ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 )
2	1	exp41	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )
3	2	adantl	⊢ ( ( 𝜂 ∧ 𝜑 ) → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )
4	3	imp41	⊢ ( ( ( ( ( 𝜂 ∧ 𝜑 ) ∧ 𝜓 ) ∧ 𝜒 ) ∧ 𝜃 ) → 𝜏 )