Theorem intnan 937

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 668	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 619  ax-in2 620

This theorem is referenced by:  bianfi  956  rabsnif  3763  axnul  4240  fodjum  7450  nninfwlporlemd  7476  iftrueb01  7546  pw1if  7548  2omotaplemap  7587  xrltnr  10131  nltmnf  10140  3lcm2e6woprm  12808  6lcm4e12  12809  eupth2lem1  16579  subctctexmid  16900