Theorem syl3anr2 1235

Description: A syllogism inference. (Contributed by NM, 1-Aug-2007.)

Hypotheses

Ref	Expression
syl3anr2.1	⊢ (φ → θ)
syl3anr2.2	⊢ ((χ ∧ (ψ ∧ θ ∧ τ)) → η)

Assertion

Ref	Expression
syl3anr2	⊢ ((χ ∧ (ψ ∧ φ ∧ τ)) → η)

Proof of Theorem syl3anr2

Step	Hyp	Ref	Expression
1		syl3anr2.1	. . 3 ⊢ (φ → θ)
2		syl3anr2.2	. . . 4 ⊢ ((χ ∧ (ψ ∧ θ ∧ τ)) → η)
3	2	ancoms 439	. . 3 ⊢ (((ψ ∧ θ ∧ τ) ∧ χ) → η)
4	1, 3	syl3anl2 1231	. 2 ⊢ (((ψ ∧ φ ∧ τ) ∧ χ) → η)
5	4	ancoms 439	1 ⊢ ((χ ∧ (ψ ∧ φ ∧ τ)) → 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)