Theorem ad5ant14 757

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 715	. 2 ⊢ (((𝜑 ∧ 𝜃) ∧ 𝜓) → 𝜒)
3	2	ad4ant13 751	1 ⊢ (((((𝜑 ∧ 𝜃) ∧ 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:  leexp1a  14086  cpmatinvcl  22635  restcld  23090  ustuqtop3  24161  legval  28565  ccatws1f1o  32941  mplvrpmrhm  33597  lssdimle  33643  zarcls1  33905  lindsenlbs  37678  matunitlindflem1  37679  modelaxrep  45101  xrralrecnnle  45508  limclner  45776  limsupub2  45937  xlimliminflimsup  45987  pimdecfgtioo  46842  pimincfltioo  46843