Theorem exp45 438

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

Hypothesis

Ref	Expression
exp45.1	⊢ ((𝜑 ∧ (𝜓 ∧ (𝜒 ∧ 𝜃))) → 𝜏)

Assertion

Ref	Expression
exp45	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Proof of Theorem exp45

Step	Hyp	Ref	Expression
1		exp45.1	. . 3 ⊢ ((𝜑 ∧ (𝜓 ∧ (𝜒 ∧ 𝜃))) → 𝜏)
2	1	exp32 420	. 2 ⊢ (𝜑 → (𝜓 → ((𝜒 ∧ 𝜃) → 𝜏)))
3	2	exp4a 431	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:  oaass  8600  zorn2lem4  10540  zorn2lem7  10543  iscatd2  17725  fgss2  23883  alexsubALTlem4  24059  grporcan  30538  spansncvi  31672  mdsymlem5  32427  riotasv3d  38962  cvratlem  39424  hbtlem2  43141