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Mirrors > Home > NFE Home > Th. List > bianfi | GIF version |
Description: A wff conjoined with falsehood is false. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 26-Nov-2012.) |
Ref | Expression |
---|---|
bianfi.1 | ⊢ ¬ φ |
Ref | Expression |
---|---|
bianfi | ⊢ (φ ↔ (ψ ∧ φ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bianfi.1 | . 2 ⊢ ¬ φ | |
2 | 1 | intnan 880 | . 2 ⊢ ¬ (ψ ∧ φ) |
3 | 1, 2 | 2false 339 | 1 ⊢ (φ ↔ (ψ ∧ φ)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 176 ∧ wa 358 |
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 177 df-an 360 |
This theorem is referenced by: in0 3576 |
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