Theorem ad5ant15 771

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
ad5ant15	⊢ (((((𝜑 ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜓) → 𝜒)

Proof of Theorem ad5ant15

Step	Hyp	Ref	Expression
1		ad5ant2.1	. . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)
2	1	adantlr 728	. 2 ⊢ (((𝜑 ∧ 𝜃) ∧ 𝜓) → 𝜒)
3	2	ad4ant14 765	1 ⊢ (((((𝜑 ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜓) → 𝜒)

This proof depends on syntax axioms:   → wi 4   ∧ wa 401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by:  summolem2  15882  ntrivcvg  16066  xkoccn  23938  abelthlem8  26766  rpvmasum2  27839  mulog2sumlem2  27862  f1otrge  29449  nn0xmulclb  33363  intlidl  33970  ply1degltdimlem  34254  fedgmul  34263  cos9thpiminplylem2  34415  signstfvneq0  35201  breprexplemc  35261  mblfinlem2  38577  supxrgelem  46349  supxrge  46350  rexabslelem  46428  uzub  46441  smflimlem4  47784  grimcnv  48986  iinfsubc  50166