Theorem intnanr 931

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 109	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜑)
3	1, 2	mto 663	1 ⊢ ¬ (𝜑 ∧ 𝜓)

Syntax hints:  ¬ wn 3   ∧ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-in1 615  ax-in2 616

This theorem is referenced by:  rab0  3476  co02  5180  frec0g  6452  djulclb  7116  xrltnr  9848  pnfnlt  9856  nltmnf  9857  0g0  12962  if0ab  15367