Theorem ad5ant24 761

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 715	. 2 ⊢ (((𝜃 ∧ 𝜑) ∧ 𝜓) → 𝜒)
3	2	ad4ant13 752	1 ⊢ (((((𝜃 ∧ 𝜑) ∧ 𝜏) ∧ 𝜓) ∧ 𝜂) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 395

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 207  df-an 396

This theorem is referenced by:  omlimcl  8513  cofsmo  10191  leexp1a  14137  natpropd  17946  mhpmulcl  22115  isucn2  24243  metust  24523  hpgerlem  28833  clwlkclwwlklem2a4  30067  cyc3genpm  33213  nsgqusf1olem1  33473  1arithufdlem2  33605  ist0cld  33977  matunitlindflem1  37937  rexabslelem  45846