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Theorem syl1111anc 841
Description: Four-hypothesis elimination deduction for an assertion with a singleton virtual hypothesis collection. Similar to syl112anc 1376 except the unification theorem uses left-nested conjunction. (Contributed by Alan Sare, 17-Oct-2017.)
Hypotheses
Ref Expression
syl1111anc.1 (𝜑𝜓)
syl1111anc.2 (𝜑𝜒)
syl1111anc.3 (𝜑𝜃)
syl1111anc.4 (𝜑𝜏)
syl1111anc.5 ((((𝜓𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜂)
Assertion
Ref Expression
syl1111anc (𝜑𝜂)

Proof of Theorem syl1111anc
StepHypRef Expression
1 syl1111anc.1 . . 3 (𝜑𝜓)
2 syl1111anc.2 . . 3 (𝜑𝜒)
31, 2jca 511 . 2 (𝜑 → (𝜓𝜒))
4 syl1111anc.3 . 2 (𝜑𝜃)
5 syl1111anc.4 . 2 (𝜑𝜏)
6 syl1111anc.5 . 2 ((((𝜓𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜂)
73, 4, 5, 6syl21anc 838 1 (𝜑𝜂)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395
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 207  df-an 396
This theorem is referenced by:  mpsyl4anc  843  ucnima  24290  f1otrge  28880  swrdf1  32941  mgcf1o  32993  chnind  33001  gsumfs2d  33058  cycpmrn  33163  linds2eq  33409  rhmimaidl  33460  idlmulssprm  33470  isprmidlc  33475  prmidlc  33476  qsidomlem2  33481  ply1unit  33600  lbsdiflsp0  33677  extdg1id  33716  3cubeslem1  42695  cantnftermord  43333  sineq0ALT  44957  cncfshift  45889  cncfperiod  45894
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