Theorem 3exp2 1249

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 1248	1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏))))

Syntax hints:   → wi 4   ∧ wa 104   ∧ w3a 1002

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 1004

This theorem is referenced by:  3anassrs  1253  po2nr  4399  fliftfund  5920  tfrlemibxssdm  6471  tfr1onlembxssdm  6487  tfrcllembxssdm  6500  imasmnd2  13480  grpinveu  13566  grpid  13567  grpasscan1  13591  imasgrp2  13642  imasrng  13914  imasring  14022  islmodd  14251  islssmd  14317  mulgghm2  14566  isxmetd  15015  dvidlemap  15359  dvidrelem  15360  dvidsslem  15361