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  5610  tz7.7  6332  oalimcl  8475  unbenlem  16820  rnelfm  23869  conway  27741  uspgr2wlkeqi  29627  1pthon2v  30131  spansncvi  31630  atom1d  32331  chirredlem3  32370  finminlem  36358  cvlcvr1  39384  lhpexle2lem  40054  trlord  40614  cdlemkid4  40979  dihord6apre  41301  dihglbcpreN  41345