Theorem intnan 934

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 666	1 ⊢ ¬ (𝜓 ∧ 𝜑)

Syntax hints:  ¬ wn 3   ∧ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 107  ax-in1 617  ax-in2 618

This theorem is referenced by:  bianfi  953  rabsnif  3736  axnul  4212  fodjum  7336  nninfwlporlemd  7362  iftrueb01  7431  pw1if  7433  2omotaplemap  7466  xrltnr  10004  nltmnf  10013  3lcm2e6woprm  12648  6lcm4e12  12649  subctctexmid  16537