Theorem exp42 427

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

Hypothesis

Ref	Expression
exp42.1	⊢ (((𝜑 ∧ (𝜓 ∧ 𝜒)) ∧ 𝜃) → 𝜏)

Assertion

Ref	Expression
exp42	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Proof of Theorem exp42

Step	Hyp	Ref	Expression
1		exp42.1	. . 3 ⊢ (((𝜑 ∧ (𝜓 ∧ 𝜒)) ∧ 𝜃) → 𝜏)
2	1	exp31 411	. 2 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → (𝜃 → 𝜏)))
3	2	expd 405	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Syntax hints:   → wi 4   ∧ wa 385

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 199  df-an 386

This theorem is referenced by:  isofrlem  6818  f1ocnv2d  7120  oelim  7854  zorn2lem7  9612  addid1  10506  initoeu1  16975  termoeu1  16982  issubg4  17926  lmodvsdir  19205  lmodvsass  19206  gsummatr01lem4  20791  dvfsumrlim3  24137  wwlksext2clwwlk  27373  shscli  28701  f1o3d  29950  slmdvsdir  30285  slmdvsass  30286  lshpcmp  35009