Theorem intnan 871

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 108	. 2 ⊢ ((𝜓 ∧ 𝜑) → 𝜑)
3	1, 2	mto 620	1 ⊢ ¬ (𝜓 ∧ 𝜑)

Syntax hints:  ¬ wn 3   ∧ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 105  ax-in1 576  ax-in2 577

This theorem is referenced by:  bianfi  888  axnul  3903  xrltnr  8855  nltmnf  8863  3lcm2e6woprm  10468  6lcm4e12  10469