Theorem intnan 880

Description: Introduction of conjunct inside of a contradiction. (Contributed by NM, 16-Sep-1993.)

Hypothesis

Ref	Expression
intnan.1	⊢ ¬ φ

Assertion

Ref	Expression
intnan	⊢ ¬ (ψ ∧ φ)

Proof of Theorem intnan

Step	Hyp	Ref	Expression
1		intnan.1	. 2 ⊢ ¬ φ
2		simpr 447	. 2 ⊢ ((ψ ∧ φ) → φ)
3	1, 2	mto 167	1 ⊢ ¬ (ψ ∧ φ)

Syntax hints:  ¬ wn 3   ∧ wa 358

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  bianfi  891  truanfal  1337  indifdir  3511  eqtfinrelk  4486  co01  5093  imadif  5171  xpnedisj  5513  2p1e3c  6156  nnc3n3p1  6278