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Theorem ad5ant2345 1490
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.)
Hypothesis
Ref Expression
ad5ant2345.1 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏)
Assertion
Ref Expression
ad5ant2345 (((((𝜂𝜑) ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏)

Proof of Theorem ad5ant2345
StepHypRef Expression
1 ad5ant2345.1 . . . 4 ((((𝜑𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏)
21exp41 426 . . 3 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
32adantl 474 . 2 ((𝜂𝜑) → (𝜓 → (𝜒 → (𝜃𝜏))))
43imp41 417 1 (((((𝜂𝜑) ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 385
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 199  df-an 386
This theorem is referenced by:  mblfinlem2  33935  liminflelimsuplem  40746  climxlim2lem  40810  iundjiun  41415
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