Theorem exp41 384

Description: An exportation inference.

Hypothesis

Ref	Expression
exp41.1	⊢ ((((φ ⋀ ψ) ⋀ χ) ⋀ θ) → τ)

Assertion

Ref	Expression
exp41	⊢ (φ → (ψ → (χ → (θ → τ))))

Proof of Theorem exp41

Step	Hyp	Ref	Expression
1		exp41.1	. . 3 ⊢ ((((φ ⋀ ψ) ⋀ χ) ⋀ θ) → τ)
2	1	ex 373	. 2 ⊢ (((φ ⋀ ψ) ⋀ χ) → (θ → τ))
3	2	exp31 378	1 ⊢ (φ → (ψ → (χ → (θ → τ))))

Syntax hints:   → wi 3   ⋀ wa 223

This theorem is referenced by:  tz7.49 3973  supxrun 6091  ser1add2 6521  fsumsplit 7034  fsumrev 7043  climshft 7118  fsum0diag4 7275  infxpidmlem12 7578  iscncl 7779  bcthlem29 8036  osumlem4 9588  branmfnt 10045

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

Copyright terms: Public domain