Theorem exp31 587

Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)

Hypothesis

Ref	Expression
exp31.1	⊢ (((φ ∧ ψ) ∧ χ) → θ)

Assertion

Ref	Expression
exp31	⊢ (φ → (ψ → (χ → θ)))

Proof of Theorem exp31

Step	Hyp	Ref	Expression
1		exp31.1	. . 3 ⊢ (((φ ∧ ψ) ∧ χ) → θ)
2	1	ex 423	. 2 ⊢ ((φ ∧ ψ) → (χ → θ))
3	2	ex 423	1 ⊢ (φ → (ψ → (χ → θ)))

This proof depends on syntax axioms:   → wi 4   ∧ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by:  exp41  593  exp42  594  expl  601  exbiri  605  anasss  628  an31s  781  3impa  1146  exp516  1171  ax11indalem  2197  ax11inda2ALT  2198  nndisjeq  4430  dffo3  5423  fconstfv  5457