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Mirrors > Home > ILE Home > Th. List > intnanrd | GIF version |
Description: Introduction of conjunct inside of a contradiction. (Contributed by NM, 10-Jul-2005.) |
Ref | Expression |
---|---|
intnand.1 | ⊢ (𝜑 → ¬ 𝜓) |
Ref | Expression |
---|---|
intnanrd | ⊢ (𝜑 → ¬ (𝜓 ∧ 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | intnand.1 | . 2 ⊢ (𝜑 → ¬ 𝜓) | |
2 | simpl 108 | . 2 ⊢ ((𝜓 ∧ 𝜒) → 𝜓) | |
3 | 1, 2 | nsyl 602 | 1 ⊢ (𝜑 → ¬ (𝜓 ∧ 𝜒)) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∧ wa 103 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-in1 588 ax-in2 589 |
This theorem is referenced by: dcan 903 bianfd 917 frecabcl 6264 frecsuclem 6271 xrrebnd 9570 fzpreddisj 9819 iseqf1olemqk 10235 gcdsupex 11573 gcdsupcl 11574 nndvdslegcd 11581 divgcdnn 11590 sqgcd 11644 coprm 11749 ctiunctlemudc 11877 |
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