Theorem mpanlr1 667

Description: An inference based on modus ponens. (Contributed by NM, 30-Dec-2004.) (Proof shortened by Wolf Lammen, 7-Apr-2013.)

Hypotheses

Ref	Expression
mpanlr1.1	⊢ ψ
mpanlr1.2	⊢ (((φ ∧ (ψ ∧ χ)) ∧ θ) → τ)

Assertion

Ref	Expression
mpanlr1	⊢ (((φ ∧ χ) ∧ θ) → τ)

Proof of Theorem mpanlr1

Step	Hyp	Ref	Expression
1		mpanlr1.1	. . 3 ⊢ ψ
2	1	jctl 525	. 2 ⊢ (χ → (ψ ∧ χ))
3		mpanlr1.2	. 2 ⊢ (((φ ∧ (ψ ∧ χ)) ∧ θ) → τ)
4	2, 3	sylanl2 632	1 ⊢ (((φ ∧ χ) ∧ θ) → 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: (None)