MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ad5ant14 Structured version   Visualization version   GIF version

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 ((𝜑𝜓) → 𝜒)
Assertion
Ref Expression
ad5ant14 (((((𝜑𝜃) ∧ 𝜏) ∧ 𝜓) ∧ 𝜂) → 𝜒)

Proof of Theorem ad5ant14
StepHypRef Expression
1 ad5ant2.1 . . 3 ((𝜑𝜓) → 𝜒)
21adantlr 714 . 2 (((𝜑𝜃) ∧ 𝜓) → 𝜒)
32ad4ant13 750 1 (((((𝜑𝜃) ∧ 𝜏) ∧ 𝜓) ∧ 𝜂) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399
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 400
This theorem is referenced by:  leexp1a  13544  cpmatinvcl  21325  restcld  21780  ustuqtop3  22852  legval  26381  lssdimle  31066  lindsenlbs  34997  matunitlindflem1  34998  xrralrecnnle  41943  limclner  42219  limsupub2  42380  xlimliminflimsup  42430  pimdecfgtioo  43278  pimincfltioo  43279
  Copyright terms: Public domain W3C validator