Theorem exp44 437

Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)

Hypothesis

Ref	Expression
exp44.1	⊢ ((𝜑 ∧ ((𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜏)

Assertion

Ref	Expression
exp44	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Proof of Theorem exp44

Step	Hyp	Ref	Expression
1		exp44.1	. . 3 ⊢ ((𝜑 ∧ ((𝜓 ∧ 𝜒) ∧ 𝜃)) → 𝜏)
2	1	exp32 420	. 2 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → (𝜃 → 𝜏)))
3	2	expd 415	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

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:  wefrc  5625  tz7.7  6349  oalimcl  8495  unbenlem  16879  rnelfm  23918  conway  27771  uspgr2wlkeqi  29716  1pthon2v  30223  spansncvi  31723  atom1d  32424  chirredlem3  32463  finminlem  36500  regsfromregtco  36720  cvlcvr1  39785  lhpexle2lem  40455  trlord  41015  cdlemkid4  41380  dihord6apre  41702  dihglbcpreN  41746