Theorem imp43 288

Description: An importation inference.

Hypothesis

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

Assertion

Ref	Expression
imp43	⊢ (((φ ∧ ψ) ∧ (χ ∧ θ)) → τ)

Proof of Theorem imp43

Step	Hyp	Ref	Expression
1		imp4.1	. . 3 ⊢ (φ → (ψ → (χ → (θ → τ))))
2	1	imp4b 283	. 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:  sotri 2630  tfrlem2 2950  fundmen 3333  fiint 3445  ltexprlem6 3941  prlem936b 3948  infxpidmlem11 4943  spansneleq 5475  elspansn4t 5478

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