Theorem exp42 438

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 422	. 2 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → (𝜃 → 𝜏)))
3	2	expd 418	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Syntax hints:   → wi 4   ∧ wa 398

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 209  df-an 399

This theorem is referenced by:  isofrlem  7096  f1ocnv2d  7401  oelim  8162  zorn2lem7  9927  addid1  10823  initoeu1  17274  termoeu1  17281  issubg4  18301  lmodvsdir  19661  lmodvsass  19662  gsummatr01lem4  21270  dvfsumrlim3  24633  wwlksext2clwwlk  27839  shscli  29097  f1o3d  30375  slmdvsdir  30848  slmdvsass  30849  lshpcmp  36128