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Mirrors > Home > MPE Home > Th. List > intn3an3d | Structured version Visualization version GIF version |
Description: Introduction of a triple conjunct inside a contradiction. (Contributed by FL, 27-Dec-2007.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
intn3and.1 | ⊢ (𝜑 → ¬ 𝜓) |
Ref | Expression |
---|---|
intn3an3d | ⊢ (𝜑 → ¬ (𝜒 ∧ 𝜃 ∧ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | intn3and.1 | . 2 ⊢ (𝜑 → ¬ 𝜓) | |
2 | simp3 1139 | . 2 ⊢ ((𝜒 ∧ 𝜃 ∧ 𝜓) → 𝜓) | |
3 | 1, 2 | nsyl 140 | 1 ⊢ (𝜑 → ¬ (𝜒 ∧ 𝜃 ∧ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∧ w3a 1088 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 206 df-an 398 df-3an 1090 |
This theorem is referenced by: frxp2 8130 frxp3 8137 en3lp 9609 winainflem 10688 ccatalpha 14543 clwwlk 29236 nlimsuc 42192 gtnelioc 44204 icccncfext 44603 fourierdlem10 44833 |
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