MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ad4ant123 Structured version   Visualization version   GIF version

Theorem ad4ant123 1173
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 14-Apr-2022.)
Hypothesis
Ref Expression
ad4ant3.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
ad4ant123 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜏) → 𝜃)

Proof of Theorem ad4ant123
StepHypRef Expression
1 ad4ant3.1 . . 3 ((𝜑𝜓𝜒) → 𝜃)
213expa 1119 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
32adantr 482 1 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜏) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 397  w3a 1088
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 206  df-an 398  df-3an 1090
This theorem is referenced by:  fin1a2lem11  10354  wrdl3s3  14860  usgr2pthlem  28760  grplsmid  32240  satfrel  34025  uzindd  40484  4animp1  42871  hspmbllem2  44958
  Copyright terms: Public domain W3C validator