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Theorem ad5ant15 1294
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.)
Hypothesis
Ref Expression
ad5ant15.1 ((𝜑𝜓) → 𝜒)
Assertion
Ref Expression
ad5ant15 (((((𝜑𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜓) → 𝜒)

Proof of Theorem ad5ant15
StepHypRef Expression
1 ad5ant15.1 . . . . . . . . . 10 ((𝜑𝜓) → 𝜒)
21ex 448 . . . . . . . . 9 (𝜑 → (𝜓𝜒))
322a1dd 48 . . . . . . . 8 (𝜑 → (𝜓 → (𝜃 → (𝜏𝜒))))
43a1ddd 77 . . . . . . 7 (𝜑 → (𝜓 → (𝜃 → (𝜂 → (𝜏𝜒)))))
54com45 94 . . . . . 6 (𝜑 → (𝜓 → (𝜃 → (𝜏 → (𝜂𝜒)))))
65com23 83 . . . . 5 (𝜑 → (𝜃 → (𝜓 → (𝜏 → (𝜂𝜒)))))
76com34 88 . . . 4 (𝜑 → (𝜃 → (𝜏 → (𝜓 → (𝜂𝜒)))))
87com45 94 . . 3 (𝜑 → (𝜃 → (𝜏 → (𝜂 → (𝜓𝜒)))))
98imp 443 . 2 ((𝜑𝜃) → (𝜏 → (𝜂 → (𝜓𝜒))))
109imp41 616 1 (((((𝜑𝜃) ∧ 𝜏) ∧ 𝜂) ∧ 𝜓) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382
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
This theorem is referenced by:  mblfinlem2  32420  supxrgelem  38298  supxrge  38299  smflimlem4  39464
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