Theorem syl3anr1 1234

Description: A syllogism inference. (Contributed by NM, 31-Jul-2007.)

Hypotheses

Ref	Expression
syl3anr1.1	⊢ (φ → ψ)
syl3anr1.2	⊢ ((χ ∧ (ψ ∧ θ ∧ τ)) → η)

Assertion

Ref	Expression
syl3anr1	⊢ ((χ ∧ (φ ∧ θ ∧ τ)) → η)

Proof of Theorem syl3anr1

Step	Hyp	Ref	Expression
1		syl3anr1.1	. . 3 ⊢ (φ → ψ)
2	1	3anim1i 1138	. 2 ⊢ ((φ ∧ θ ∧ τ) → (ψ ∧ θ ∧ τ))
3		syl3anr1.2	. 2 ⊢ ((χ ∧ (ψ ∧ θ ∧ τ)) → η)
4	2, 3	sylan2 460	1 ⊢ ((χ ∧ (φ ∧ θ ∧ τ)) → η)

Syntax hints:   → wi 4   ∧ wa 358   ∧ w3a 934

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  df-3an 936

This theorem is referenced by: (None)