Theorem intnanrd 883

Description: Introduction of conjunct inside of a contradiction. (Contributed by NM, 10-Jul-2005.)

Hypothesis

Ref	Expression
intnand.1	⊢ (φ → ¬ ψ)

Assertion

Ref	Expression
intnanrd	⊢ (φ → ¬ (ψ ∧ χ))

Proof of Theorem intnanrd

Step	Hyp	Ref	Expression
1		intnand.1	. 2 ⊢ (φ → ¬ ψ)
2		simpl 443	. 2 ⊢ ((ψ ∧ χ) → ψ)
3	1, 2	nsyl 113	1 ⊢ (φ → ¬ (ψ ∧ χ))

Syntax hints:  ¬ wn 3   → 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:  bianfd  892  tfinltfin  4501