Theorem ee10 1376

Description: e10 in set.mm without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011.) TODO: this is frequently used; come up with better label.

Hypotheses

Ref	Expression
ee10.1	⊢ (φ → ψ)
ee10.2	⊢ χ
ee10.3	⊢ (ψ → (χ → θ))

Assertion

Ref	Expression
ee10	⊢ (φ → θ)

Proof of Theorem ee10

Step	Hyp	Ref	Expression
1		ee10.1	. 2 ⊢ (φ → ψ)
2		ee10.2	. . 3 ⊢ χ
3		ee10.3	. . 3 ⊢ (ψ → (χ → θ))
4	2, 3	mpi 16	. 2 ⊢ (ψ → θ)
5	1, 4	syl 15	1 ⊢ (φ → θ)

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  ceqsex  2894  moeq3  3014