Theorem intnan 941

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 110	. 2 ⊢ ((𝜓 ∧ 𝜑) → 𝜑)
3	1, 2	mto 672	1 ⊢ ¬ (𝜓 ∧ 𝜑)

This proof depends on syntax axioms:  ¬ wn 3   ∧ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 107  ax-in1 623  ax-in2 624

This theorem is used by:  bianfi  960  rabsnif  3778  axnul  4258  fodjum  7487  nninfwlporlemd  7513  iftrueb01  7583  pw1if  7585  2omotaplemap  7624  xrltnr  10192  nltmnf  10201  3lcm2e6woprm  12883  6lcm4e12  12884  eupth2lem1  16865  subctctexmid  17196