Theorem ad4ant134 1193

Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 14-Apr-2022.)

Hypothesis

Ref	Expression
ad4ant3.1	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

Assertion

Ref	Expression
ad4ant134	⊢ ((((𝜑 ∧ 𝜏) ∧ 𝜓) ∧ 𝜒) → 𝜃)

Proof of Theorem ad4ant134

Step	Hyp	Ref	Expression
1		ad4ant3.1	. . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)
2	1	3expa 1136	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃)
3	2	adantllr 731	1 ⊢ ((((𝜑 ∧ 𝜏) ∧ 𝜓) ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ wa 400   ∧ w3a 1103

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 210  df-an 401  df-3an 1105

This theorem is referenced by:  ad5ant245  1384  ad5ant134OLD  1393  ad5ant135OLD  1395  ad5ant145  1396  ralxfrd2  5383  gruwun  10793  lemul12b  12067  initoeu1  18063  termoeu1  18070  quscrng  21423  metss  24665  wlkswwlksf1o  30228  climxlim2lem  46559  smflimlem4  47488  isubgr3stgrlem8  48738