Theorem ee02 1377

Description: e02 in set.mm without virtual deductions. (Contributed by Alan Sare, 22-Jul-2012.) (New usage is discouraged.) TODO: decide if this is worth keeping.

Hypotheses

Ref	Expression
ee02.1	⊢ φ
ee02.2	⊢ (ψ → (χ → θ))
ee02.3	⊢ (φ → (θ → τ))

Assertion

Ref	Expression
ee02	⊢ (ψ → (χ → τ))

Proof of Theorem ee02

Step	Hyp	Ref	Expression
1		ee02.1	. . 3 ⊢ φ
2	1	a1i 10	. 2 ⊢ (ψ → φ)
3		ee02.2	. 2 ⊢ (ψ → (χ → θ))
4		ee02.3	. 2 ⊢ (φ → (θ → τ))
5	2, 3, 4	sylsyld 52	1 ⊢ (ψ → (χ → 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:  fvopab3ig  5388