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Theorem ad5ant13 753
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
ad5ant13 (((((𝜑𝜃) ∧ 𝜓) ∧ 𝜏) ∧ 𝜂) → 𝜒)

Proof of Theorem ad5ant13
StepHypRef Expression
1 ad5ant2.1 . . 3 ((𝜑𝜓) → 𝜒)
21adantlr 711 . 2 (((𝜑𝜃) ∧ 𝜓) → 𝜒)
32ad2antrr 722 1 (((((𝜑𝜃) ∧ 𝜓) ∧ 𝜏) ∧ 𝜂) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396
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 208  df-an 397
This theorem is referenced by:  natpropd  17236  ghmcmn  18872  ustuqtop2  22769  tocyccntz  30703  matunitlindflem1  34758  supxrgelem  41473  xrralrecnnle  41521  limsupvaluz2  41887  supcnvlimsup  41889  meaiuninc3v  42635  smfaddlem1  42908  smflimlem4  42919
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