Theorem imp42 287

Description: An importation inference.

Hypothesis

Ref	Expression
imp4.1	⊢ (φ → (ψ → (χ → (θ → τ))))

Assertion

Ref	Expression
imp42	⊢ (((φ ∧ (ψ ∧ χ)) ∧ θ) → τ)

Proof of Theorem imp42

Step	Hyp	Ref	Expression
1		imp4.1	. . 3 ⊢ (φ → (ψ → (χ → (θ → τ))))
2	1	imp32 281	. 2 ⊢ ((φ ∧ (ψ ∧ χ)) → (θ → τ))
3	2	imp 277	1 ⊢ (((φ ∧ (ψ ∧ χ)) ∧ θ) → τ)

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  adantlrl 314  adantlrr 315  supmo 2156  mapenlem2 3385  ltexprlem7 3942  reclem3pr 3952

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

This theorem depends on definitions:  df-bi 128  df-an 198

metamath.org