Theorem 3exp2 1251

Description: Exportation from right triple conjunction. (Contributed by NM, 26-Oct-2006.)

Hypothesis

Ref	Expression
3exp2.1	⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)) → 𝜏)

Assertion

Ref	Expression
3exp2	⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Proof of Theorem 3exp2

Step	Hyp	Ref	Expression
1		3exp2.1	. . 3 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)) → 𝜏)
2	1	ex 115	. 2 ⊢ (𝜑 → ((𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏))
3	2	3expd 1250	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 1004

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 1006

This theorem is referenced by:  3anassrs  1255  po2nr  4406  fliftfund  5938  tfrlemibxssdm  6493  tfr1onlembxssdm  6509  tfrcllembxssdm  6522  imasmnd2  13540  grpinveu  13626  grpid  13627  grpasscan1  13651  imasgrp2  13702  imasrng  13975  imasring  14083  islmodd  14313  islssmd  14379  mulgghm2  14628  isxmetd  15077  dvidlemap  15421  dvidrelem  15422  dvidsslem  15423