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Theorem 3adant1l 1177
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.) (Proof shortened by Wolf Lammen, 23-Jun-2022.)
Hypothesis
Ref Expression
ad4ant3.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
3adant1l (((𝜏𝜑) ∧ 𝜓𝜒) → 𝜃)

Proof of Theorem 3adant1l
StepHypRef Expression
1 simpr 486 . 2 ((𝜏𝜑) → 𝜑)
2 ad4ant3.1 . 2 ((𝜑𝜓𝜒) → 𝜃)
31, 2syl3an1 1164 1 (((𝜏𝜑) ∧ 𝜓𝜒) → 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:  ad5ant245  1362  cfsmolem  10261  axdc3lem4  10444  issubmnd  18648  mhmima  18702  maducoeval2  22124  cramerlem3  22173  restnlly  22968  efgh  26032  hasheuni  33021  matunitlindflem1  36422  pellex  41506  mendlmod  41868  disjf1o  43822  ssfiunibd  43954  mullimc  44267  mullimcf  44274  limclner  44302  limsupresxr  44417  liminfresxr  44418  sge0lefi  45049  isomenndlem  45181  hoicvr  45199  ovncvrrp  45215  rhmimasubrng  46678
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