Theorem ad5ant134 1367

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 1174	. 2 ⊢ ((((𝜑 ∧ 𝜏) ∧ 𝜓) ∧ 𝜒) → 𝜃)
3	2	adantr 481	1 ⊢ (((((𝜑 ∧ 𝜏) ∧ 𝜓) ∧ 𝜒) ∧ 𝜂) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 396   ∧ w3a 1087

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 397  df-3an 1089

This theorem is referenced by:  qsidomlem1  32486  suplesup  43886  limsupvaluz2  44291  supcnvlimsup  44293  limsupgtlem  44330  xlimmnfvlem2  44386  xlimmnfv  44387  xlimpnfvlem2  44390  xlimpnfv  44391  sge0cl  44934  hspmbllem2  45180