MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ad4ant134 Structured version   Visualization version   GIF version

Theorem ad4ant134 1171
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
ad4ant134 ((((𝜑𝜏) ∧ 𝜓) ∧ 𝜒) → 𝜃)

Proof of Theorem ad4ant134
StepHypRef Expression
1 ad4ant3.1 . . 3 ((𝜑𝜓𝜒) → 𝜃)
213expa 1115 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
32adantllr 716 1 ((((𝜑𝜏) ∧ 𝜓) ∧ 𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  w3a 1084
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 396  df-3an 1086
This theorem is referenced by:  ad5ant245  1358  ad5ant134  1364  ad5ant135  1365  ad5ant145  1366  ralxfrd2  5403  gruwun  10810  lemul12b  12075  initoeu1  17973  termoeu1  17980  quscrng  21138  metss  24372  wlkswwlksf1o  29642  climxlim2lem  45133  smflimlem4  46062
  Copyright terms: Public domain W3C validator