Theorem ad5ant134 1383

Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 23-Jun-2022.) (Proof shortened by Garrett Katz, 13-Jun-2026.)

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	ad4ant123 1185	. 2 ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜂) → 𝜃)
3	2	adantl3r 760	1 ⊢ (((((𝜑 ∧ 𝜏) ∧ 𝜓) ∧ 𝜒) ∧ 𝜂) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 399   ∧ w3a 1097

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 209  df-an 400  df-3an 1099

This theorem is referenced by:  qsidomlem1  33600  suplesup  45876  limsupvaluz2  46273  supcnvlimsup  46275  limsupgtlem  46312  xlimmnfvlem2  46368  xlimmnfv  46369  xlimpnfvlem2  46372  xlimpnfv  46373  sge0cl  46916  hspmbllem2  47162