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Theorem intnan 876
Description: Introduction of conjunct inside of a contradiction. (Contributed by NM, 16-Sep-1993.)
Hypothesis
Ref Expression
intnan.1 ¬ 𝜑
Assertion
Ref Expression
intnan ¬ (𝜓𝜑)

Proof of Theorem intnan
StepHypRef Expression
1 intnan.1 . 2 ¬ 𝜑
2 simpr 108 . 2 ((𝜓𝜑) → 𝜑)
31, 2mto 623 1 ¬ (𝜓𝜑)
Colors of variables: wff set class
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 579  ax-in2 580
This theorem is referenced by:  bianfi  893  axnul  3956  fodjuomnilemm  6780  xrltnr  9219  nltmnf  9227  3lcm2e6woprm  11150  6lcm4e12  11151
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