Metamath Proof Explorer


Theorem intnanr

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

Ref Expression
Hypothesis intnan.1
|- -. ph
Assertion intnanr
|- -. ( ph /\ ps )

Proof

Step Hyp Ref Expression
1 intnan.1
 |-  -. ph
2 simpl
 |-  ( ( ph /\ ps ) -> ph )
3 1 2 mto
 |-  -. ( ph /\ ps )