Theorem imdistanri 672

Description: Distribution of implication with conjunction. (Contributed by NM, 8-Jan-2002.)

Hypothesis

Ref	Expression
imdistanri.1	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
imdistanri	⊢ ((ψ ∧ φ) → (χ ∧ φ))

Proof of Theorem imdistanri

Step	Hyp	Ref	Expression
1		imdistanri.1	. . 3 ⊢ (φ → (ψ → χ))
2	1	com12 27	. 2 ⊢ (ψ → (φ → χ))
3	2	impac 604	1 ⊢ ((ψ ∧ φ) → (χ ∧ φ))

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

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

This theorem is used by: (None)