Theorem intnanr 881

Description: Introduction of conjunct inside of a contradiction. (Contributed by NM, 3-Apr-1995.)

Hypothesis

Ref	Expression
intnan.1	⊢ ¬ φ

Assertion

Ref	Expression
intnanr	⊢ ¬ (φ ∧ ψ)

Proof of Theorem intnanr

Step	Hyp	Ref	Expression
1		intnan.1	. 2 ⊢ ¬ φ
2		simpl 443	. 2 ⊢ ((φ ∧ ψ) → φ)
3	1, 2	mto 167	1 ⊢ ¬ (φ ∧ ψ)

Syntax hints:  ¬ wn 3   ∧ 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:  falantru  1338  rab0  3572  co02  5093  fnfreclem2  6319