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Theorem ad5ant123 1350
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.)
Hypothesis
Ref Expression
ad5ant123.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
ad5ant123 (((((𝜑𝜓) ∧ 𝜒) ∧ 𝜏) ∧ 𝜂) → 𝜃)

Proof of Theorem ad5ant123
StepHypRef Expression
1 ad5ant123.1 . . . . . . 7 ((𝜑𝜓𝜒) → 𝜃)
213exp 1283 . . . . . 6 (𝜑 → (𝜓 → (𝜒𝜃)))
32a1ddd 80 . . . . 5 (𝜑 → (𝜓 → (𝜒 → (𝜏𝜃))))
43a1ddd 80 . . . 4 (𝜑 → (𝜓 → (𝜒 → (𝜂 → (𝜏𝜃)))))
54com45 97 . . 3 (𝜑 → (𝜓 → (𝜒 → (𝜏 → (𝜂𝜃)))))
65imp 444 . 2 ((𝜑𝜓) → (𝜒 → (𝜏 → (𝜂𝜃))))
76imp41 618 1 (((((𝜑𝜓) ∧ 𝜒) ∧ 𝜏) ∧ 𝜂) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 383  w3a 1054
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 385  df-3an 1056
This theorem is referenced by: (None)
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