Theorem intnanr 838

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 102	. 2 ⊢ ((φ ∧ ψ) → φ)
3	1, 2	mto 587	1 ⊢ ¬ (φ ∧ ψ)

Syntax hints:  ¬ wn 3   ∧ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-in1 544  ax-in2 545

This theorem is referenced by:  rab0  3240  co02  4777  frec0g  5922  xrltnr  8471  pnfnlt  8478  nltmnf  8479