Theorem ee12an 1363

Description: e12an in set.mm without virtual deduction connectives. Special theorem needed for Alan Sare's virtual deduction translation tool. (Contributed by Alan Sare, 28-Oct-2011.) TODO: this is frequently used; come up with better label.

Hypotheses

Ref	Expression
ee12an.1	⊢ (φ → ψ)
ee12an.2	⊢ (φ → (χ → θ))
ee12an.3	⊢ ((ψ ∧ θ) → τ)

Assertion

Ref	Expression
ee12an	⊢ (φ → (χ → τ))

Proof of Theorem ee12an

Step	Hyp	Ref	Expression
1		ee12an.2	. . 3 ⊢ (φ → (χ → θ))
2		ee12an.1	. . 3 ⊢ (φ → ψ)
3	1, 2	jctild 527	. 2 ⊢ (φ → (χ → (ψ ∧ θ)))
4		ee12an.3	. 2 ⊢ ((ψ ∧ θ) → τ)
5	3, 4	syl6 29	1 ⊢ (φ → (χ → τ))

Syntax hints:   → wi 4   ∧ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

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

This theorem is referenced by:  dfsb2  2055