Theorem intnanr 517

Description: Introduction of conjunct inside of a contradiction.

Hypothesis

Ref	Expression
intnanr.1	⊢ ¬ φ

Assertion

Ref	Expression
intnanr	⊢ ¬ (φ ∧ ψ)

Proof of Theorem intnanr

Step	Hyp	Ref	Expression
1		intnanr.1	. 2 ⊢ ¬ φ
2		pm3.26 256	. 2 ⊢ ((φ ∧ ψ) → φ)
3	1, 2	mto 93	1 ⊢ ¬ (φ ∧ ψ)

Syntax hints:  ¬ wn 1   ∧ wa 196

This theorem is referenced by:  rab0 1718  0nelxp 2475  co02 2663  ruclem29 4913

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

metamath.org