Theorem intnan 914

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 109	. 2 ⊢ ((𝜓 ∧ 𝜑) → 𝜑)
3	1, 2	mto 651	1 ⊢ ¬ (𝜓 ∧ 𝜑)

Syntax hints:  ¬ wn 3   ∧ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 106  ax-in1 603  ax-in2 604

This theorem is referenced by:  bianfi  931  axnul  4053  fodjum  7018  xrltnr  9566  nltmnf  9574  3lcm2e6woprm  11767  6lcm4e12  11768  subctctexmid  13196