Theorem ad5ant14 770

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
ad5ant14	⊢ (((((𝜑 ∧ 𝜃) ∧ 𝜏) ∧ 𝜓) ∧ 𝜂) → 𝜒)

Proof of Theorem ad5ant14

Step	Hyp	Ref	Expression
1		ad5ant2.1	. . 3 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)
2	1	adantlr 728	. 2 ⊢ (((𝜑 ∧ 𝜃) ∧ 𝜓) → 𝜒)
3	2	ad4ant13 764	1 ⊢ (((((𝜑 ∧ 𝜃) ∧ 𝜏) ∧ 𝜓) ∧ 𝜂) → 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:  leexp1a  14298  lindsenlbs  22137  matunitlindflem1  22974  cpmatinvcl  23015  restcld  23470  ustuqtop3  24542  legval  29029  ccatws1f1o  33496  mplvrpmrhm  34161  esplyfval1  34187  lssdimle  34222  zarcls1  34483  modelaxrep  45923  xrralrecnnle  46338  limclner  46605  limsupub2  46766  xlimliminflimsup  46816  pimdecfgtioo  47671  pimincfltioo  47672