Theorem ad5ant134 1365

Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)

Hypothesis

Ref	Expression
ad5ant.1	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

Assertion

Ref	Expression
ad5ant134	⊢ (((((𝜑 ∧ 𝜏) ∧ 𝜓) ∧ 𝜒) ∧ 𝜂) → 𝜃)

Proof of Theorem ad5ant134

Step	Hyp	Ref	Expression
1		ad5ant.1	. . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)
2	1	ad4ant134 1172	. 2 ⊢ ((((𝜑 ∧ 𝜏) ∧ 𝜓) ∧ 𝜒) → 𝜃)
3	2	adantr 480	1 ⊢ (((((𝜑 ∧ 𝜏) ∧ 𝜓) ∧ 𝜒) ∧ 𝜂) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1085

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 396  df-3an 1087

This theorem is referenced by:  qsidomlem1  31530  suplesup  42768  limsupvaluz2  43169  supcnvlimsup  43171  limsupgtlem  43208  xlimmnfvlem2  43264  xlimmnfv  43265  xlimpnfvlem2  43268  xlimpnfv  43269  sge0cl  43809  hspmbllem2  44055