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Theorem ad5ant245 1299
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.)
Hypothesis
Ref Expression
ad5ant245.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
ad5ant245 (((((𝜏𝜑) ∧ 𝜂) ∧ 𝜓) ∧ 𝜒) → 𝜃)

Proof of Theorem ad5ant245
StepHypRef Expression
1 ad5ant245.1 . . . . 5 ((𝜑𝜓𝜒) → 𝜃)
213exp 1256 . . . 4 (𝜑 → (𝜓 → (𝜒𝜃)))
32a1i13 27 . . 3 (𝜏 → (𝜑 → (𝜂 → (𝜓 → (𝜒𝜃)))))
43imp 444 . 2 ((𝜏𝜑) → (𝜂 → (𝜓 → (𝜒𝜃))))
54imp41 617 1 (((((𝜏𝜑) ∧ 𝜂) ∧ 𝜓) ∧ 𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  w3a 1031
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 196  df-an 385  df-3an 1033
This theorem is referenced by:  matunitlindflem1  32369  nnfoctbdjlem  39142  sfprmdvdsmersenne  39853  2pthnloop  40929
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