Theorem exp42 435

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 419	. 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:  isofrlem  7288  f1ocnv2d  7613  oelim  8462  zorn2lem7  10415  addrid  11317  initoeu1  17969  termoeu1  17976  issubg4  19112  lmodvsdir  20872  lmodvsass  20873  gsummatr01lem4  22633  dvfsumrlim3  26010  wwlksext2clwwlk  30142  shscli  31403  f1o3d  32714  slmdvsdir  33292  slmdvsass  33293  lshpcmp  39448  relpfrlem  45398