Theorem intnan 516

Description: Introduction of conjunct inside of a contradiction.

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		pm3.27 260	. 2 ⊢ ((ψ ∧ φ) → φ)
3	1, 2	mto 93	1 ⊢ ¬ (ψ ∧ φ)

Syntax hints:  ¬ wn 1   ∧ wa 196

This theorem is referenced by:  imadif 2714  avril1 4523  halfnz 4586

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

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