Theorem exp4c 433

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

Hypothesis

Ref	Expression
exp4c.1	⊢ (𝜑 → (((𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜏))

Assertion

Ref	Expression
exp4c	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Proof of Theorem exp4c

Step	Hyp	Ref	Expression
1		exp4c.1	. . 3 ⊢ (𝜑 → (((𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜏))
2	1	expd 416	. 2 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) → (𝜃 → 𝜏)))
3	2	expd 416	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Syntax hints:   → wi 4   ∧ wa 396

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 208  df-an 397

This theorem is referenced by:  exp5j  446  oawordri  8017  oaordex  8025  odi  8046  pssnn  8572  alephval3  9371  dfac2b  9391  axdc4lem  9712  leexp1a  13377  wrdsymb0  13735  coprmproddvds  15824  lmodvsmmulgdi  19347  assamulgscm  19806  2ndcctbss  21735  2pthnloop  27187  wwlksnext  27346  frgrregord013  27854  atcvatlem  29841  umgr2cycllem  31951  exp5g  33205  cdleme48gfv1  37153  cdlemg6e  37239  dihord5apre  37879  dihglblem5apreN  37908  iccpartgt  43023  lmodvsmdi  43864  nn0sumshdiglemB  44115