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  5682  tz7.7  6411  oalimcl  8596  unbenlem  16941  rnelfm  23976  conway  27858  uspgr2wlkeqi  29680  1pthon2v  30181  spansncvi  31680  atom1d  32381  chirredlem3  32420  finminlem  36300  cvlcvr1  39320  lhpexle2lem  39991  trlord  40551  cdlemkid4  40916  dihord6apre  41238  dihglbcpreN  41282