Theorem imp4d 285

Description: An importation inference.

Hypothesis

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

Assertion

Ref	Expression
imp4d	⊢ (φ → ((ψ ∧ (χ ∧ θ)) → τ))

Proof of Theorem imp4d

Step	Hyp	Ref	Expression
1		imp4.1	. . 3 ⊢ (φ → (ψ → (χ → (θ → τ))))
2	1	imp4a 282	. 2 ⊢ (φ → (ψ → ((χ ∧ θ) → τ)))
3	2	imp3a 279	1 ⊢ (φ → ((ψ ∧ (χ ∧ θ)) → τ))

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  imp45 290  tfrlem8 2956  tfrlem9 2957  sqrlem20 4750

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