Theorem imp45 290

Description: An importation inference.

Hypothesis

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

Assertion

Ref	Expression
imp45	⊢ ((φ ∧ (ψ ∧ (χ ∧ θ))) → τ)

Proof of Theorem imp45

Step	Hyp	Ref	Expression
1		imp4.1	. . 3 ⊢ (φ → (ψ → (χ → (θ → τ))))
2	1	imp4d 285	. 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:  adantrrl 318  adantrrr 319  supmo 2156  prlem936b 3948  spansncv 5542  atcvatlem 5770

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