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Theorem ad5ant23 1301
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.)
Hypothesis
Ref Expression
ad5ant23.1 ((𝜑𝜓) → 𝜒)
Assertion
Ref Expression
ad5ant23 (((((𝜃𝜑) ∧ 𝜓) ∧ 𝜏) ∧ 𝜂) → 𝜒)

Proof of Theorem ad5ant23
StepHypRef Expression
1 ad5ant23.1 . . . . . . . 8 ((𝜑𝜓) → 𝜒)
21ex 450 . . . . . . 7 (𝜑 → (𝜓𝜒))
322a1dd 51 . . . . . 6 (𝜑 → (𝜓 → (𝜃 → (𝜏𝜒))))
43a1ddd 80 . . . . 5 (𝜑 → (𝜓 → (𝜃 → (𝜂 → (𝜏𝜒)))))
54com45 97 . . . 4 (𝜑 → (𝜓 → (𝜃 → (𝜏 → (𝜂𝜒)))))
65com3r 87 . . 3 (𝜃 → (𝜑 → (𝜓 → (𝜏 → (𝜂𝜒)))))
76imp 445 . 2 ((𝜃𝜑) → (𝜓 → (𝜏 → (𝜂𝜒))))
87imp41 618 1 (((((𝜃𝜑) ∧ 𝜓) ∧ 𝜏) ∧ 𝜂) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384
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 197  df-an 386
This theorem is referenced by:  frgrncvvdeqlemB  27069  matunitlindflem2  33077  rexabslelem  39144  hoidmvle  40151
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