Theorem sylan2i 636

Description: A syllogism inference. (Contributed by NM, 1-Aug-1994.)

Hypotheses

Ref	Expression
sylan2i.1	⊢ (φ → θ)
sylan2i.2	⊢ (ψ → ((χ ∧ θ) → τ))

Assertion

Ref	Expression
sylan2i	⊢ (ψ → ((χ ∧ φ) → τ))

Proof of Theorem sylan2i

Step	Hyp	Ref	Expression
1		sylan2i.1	. . 3 ⊢ (φ → θ)
2	1	a1i 10	. 2 ⊢ (ψ → (φ → θ))
3		sylan2i.2	. 2 ⊢ (ψ → ((χ ∧ θ) → τ))
4	2, 3	sylan2d 468	1 ⊢ (ψ → ((χ ∧ φ) → 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:  syl2ani  637