Theorem ee21 1375

Description: e21 in set.mm without virtual deductions. (Contributed by Alan Sare, 18-Mar-2012.) (New usage is discouraged.) TODO: decide if this is worth keeping.

Hypotheses

Ref	Expression
ee21.1	⊢ (φ → (ψ → χ))
ee21.2	⊢ (φ → θ)
ee21.3	⊢ (χ → (θ → τ))

Assertion

Ref	Expression
ee21	⊢ (φ → (ψ → τ))

Proof of Theorem ee21

Step	Hyp	Ref	Expression
1		ee21.1	. 2 ⊢ (φ → (ψ → χ))
2		ee21.2	. . 3 ⊢ (φ → θ)
3	2	a1d 22	. 2 ⊢ (φ → (ψ → θ))
4		ee21.3	. 2 ⊢ (χ → (θ → τ))
5	1, 3, 4	ee22 1362	1 ⊢ (φ → (ψ → τ))

This proof depends on syntax axioms:   → wi 4

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

This theorem is used by: (None)