Theorem ad5ant24 760

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

Hypothesis

Ref	Expression
ad5ant2.1	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Assertion

Ref	Expression
ad5ant24	⊢ (((((𝜃 ∧ 𝜑) ∧ 𝜏) ∧ 𝜓) ∧ 𝜂) → 𝜒)

Proof of Theorem ad5ant24

Step	Hyp	Ref	Expression
1		ad5ant2.1	. . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)
2	1	adantll 713	. 2 ⊢ (((𝜃 ∧ 𝜑) ∧ 𝜓) → 𝜒)
3	2	ad4ant13 750	1 ⊢ (((((𝜃 ∧ 𝜑) ∧ 𝜏) ∧ 𝜓) ∧ 𝜂) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 399

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 400

This theorem is referenced by:  omlimcl  8187  cofsmo  9680  leexp1a  13535  natpropd  17238  isucn2  22885  metust  23165  hpgerlem  26559  clwlkclwwlklem2a4  27782  cyc3genpm  30844  ist0cld  31186  matunitlindflem1  35053  rexabslelem  42055