Theorem ad5ant14 769

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 727	. 2 ⊢ (((𝜑 ∧ 𝜃) ∧ 𝜓) → 𝜒)
3	2	ad4ant13 763	1 ⊢ (((((𝜑 ∧ 𝜃) ∧ 𝜏) ∧ 𝜓) ∧ 𝜂) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 400

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

This theorem is referenced by:  leexp1a  14213  cpmatinvcl  22845  restcld  23300  ustuqtop3  24371  legval  28821  ccatws1f1o  33214  mplvrpmrhm  33884  esplyfval1  33910  lssdimle  33945  zarcls1  34206  lindsenlbs  38191  matunitlindflem1  38192  modelaxrep  45619  xrralrecnnle  46027  limclner  46294  limsupub2  46455  xlimliminflimsup  46505  pimdecfgtioo  47360  pimincfltioo  47361