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Theorem ad5ant235 1300
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.)
Hypothesis
Ref Expression
ad5ant235.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
ad5ant235 (((((𝜏𝜑) ∧ 𝜓) ∧ 𝜂) ∧ 𝜒) → 𝜃)

Proof of Theorem ad5ant235
StepHypRef Expression
1 ad5ant235.1 . . . . . . . 8 ((𝜑𝜓𝜒) → 𝜃)
213exp 1255 . . . . . . 7 (𝜑 → (𝜓 → (𝜒𝜃)))
32a1ddd 77 . . . . . 6 (𝜑 → (𝜓 → (𝜒 → (𝜏𝜃))))
43a1ddd 77 . . . . 5 (𝜑 → (𝜓 → (𝜒 → (𝜂 → (𝜏𝜃)))))
54com5r 101 . . . 4 (𝜏 → (𝜑 → (𝜓 → (𝜒 → (𝜂𝜃)))))
65com45 94 . . 3 (𝜏 → (𝜑 → (𝜓 → (𝜂 → (𝜒𝜃)))))
76imp 443 . 2 ((𝜏𝜑) → (𝜓 → (𝜂 → (𝜒𝜃))))
87imp41 616 1 (((((𝜏𝜑) ∧ 𝜓) ∧ 𝜂) ∧ 𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  w3a 1030
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 195  df-an 384  df-3an 1032
This theorem is referenced by: (None)
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