Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  ad5ant25OLD Structured version   Visualization version   GIF version

 Description: Obsolete version of ad5ant25 778 as of 14-Apr-2022. (Contributed by Alan Sare, 17-Oct-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
Assertion
Ref Expression
ad5ant25OLD (((((𝜃𝜑) ∧ 𝜏) ∧ 𝜂) ∧ 𝜓) → 𝜒)

StepHypRef Expression
1 ad5ant2.1 . . . . . . . . . 10 ((𝜑𝜓) → 𝜒)
21ex 402 . . . . . . . . 9 (𝜑 → (𝜓𝜒))
322a1dd 51 . . . . . . . 8 (𝜑 → (𝜓 → (𝜃 → (𝜏𝜒))))
43a1ddd 80 . . . . . . 7 (𝜑 → (𝜓 → (𝜃 → (𝜂 → (𝜏𝜒)))))
54com45 97 . . . . . 6 (𝜑 → (𝜓 → (𝜃 → (𝜏 → (𝜂𝜒)))))
65com3r 87 . . . . 5 (𝜃 → (𝜑 → (𝜓 → (𝜏 → (𝜂𝜒)))))
76com34 91 . . . 4 (𝜃 → (𝜑 → (𝜏 → (𝜓 → (𝜂𝜒)))))
87com45 97 . . 3 (𝜃 → (𝜑 → (𝜏 → (𝜂 → (𝜓𝜒)))))
98imp 396 . 2 ((𝜃𝜑) → (𝜏 → (𝜂 → (𝜓𝜒))))
109imp41 417 1 (((((𝜃𝜑) ∧ 𝜏) ∧ 𝜂) ∧ 𝜓) → 𝜒)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 385 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 199  df-an 386 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator