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Theorem ad5ant124 1309
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.)
Hypothesis
Ref Expression
ad5ant124.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
ad5ant124 (((((𝜑𝜓) ∧ 𝜏) ∧ 𝜒) ∧ 𝜂) → 𝜃)

Proof of Theorem ad5ant124
StepHypRef Expression
1 ad5ant124.1 . . . . . . . 8 ((𝜑𝜓𝜒) → 𝜃)
213exp 1262 . . . . . . 7 (𝜑 → (𝜓 → (𝜒𝜃)))
32a1ddd 80 . . . . . 6 (𝜑 → (𝜓 → (𝜒 → (𝜏𝜃))))
43a1ddd 80 . . . . 5 (𝜑 → (𝜓 → (𝜒 → (𝜂 → (𝜏𝜃)))))
54com45 97 . . . 4 (𝜑 → (𝜓 → (𝜒 → (𝜏 → (𝜂𝜃)))))
65com34 91 . . 3 (𝜑 → (𝜓 → (𝜏 → (𝜒 → (𝜂𝜃)))))
76imp 445 . 2 ((𝜑𝜓) → (𝜏 → (𝜒 → (𝜂𝜃))))
87imp41 618 1 (((((𝜑𝜓) ∧ 𝜏) ∧ 𝜒) ∧ 𝜂) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  w3a 1036
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  df-3an 1038
This theorem is referenced by:  hspmbllem2  40604
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