Theorem syl3anr3 1236

Description: A syllogism inference. (Contributed by NM, 23-Aug-2007.)

Hypotheses

Ref	Expression
syl3anr3.1	⊢ (φ → τ)
syl3anr3.2	⊢ ((χ ∧ (ψ ∧ θ ∧ τ)) → η)

Assertion

Ref	Expression
syl3anr3	⊢ ((χ ∧ (ψ ∧ θ ∧ φ)) → η)

Proof of Theorem syl3anr3

Step	Hyp	Ref	Expression
1		syl3anr3.1	. . 3 ⊢ (φ → τ)
2	1	3anim3i 1139	. 2 ⊢ ((ψ ∧ θ ∧ φ) → (ψ ∧ θ ∧ τ))
3		syl3anr3.2	. 2 ⊢ ((χ ∧ (ψ ∧ θ ∧ τ)) → η)
4	2, 3	sylan2 460	1 ⊢ ((χ ∧ (ψ ∧ θ ∧ φ)) → η)

This proof depends on syntax axioms:   → wi 4   ∧ wa 358   ∧ w3a 934

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360  df-3an 936

This theorem is used by: (None)