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Theorem ad5ant23 758
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
ad5ant23 (((((𝜃𝜑) ∧ 𝜓) ∧ 𝜏) ∧ 𝜂) → 𝜒)

Proof of Theorem ad5ant23
StepHypRef Expression
1 ad5ant2.1 . . 3 ((𝜑𝜓) → 𝜒)
21adantll 712 . 2 (((𝜃𝜑) ∧ 𝜓) → 𝜒)
32ad2antrr 724 1 (((((𝜃𝜑) ∧ 𝜓) ∧ 𝜏) ∧ 𝜂) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 398
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 209  df-an 399
This theorem is referenced by:  funcpropd  17162  natpropd  17238  pmtr3ncom  18595  dmatscmcl  21104  opreu2reuALT  30232  matunitlindflem2  34876  rexabslelem  41676  hoidmvle  42867
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