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Mirrors > Home > NFE Home > Th. List > mtbid | GIF version |
Description: A deduction from a biconditional, similar to modus tollens. (Contributed by NM, 26-Nov-1995.) |
Ref | Expression |
---|---|
mtbid.min | ⊢ (φ → ¬ ψ) |
mtbid.maj | ⊢ (φ → (ψ ↔ χ)) |
Ref | Expression |
---|---|
mtbid | ⊢ (φ → ¬ χ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mtbid.min | . 2 ⊢ (φ → ¬ ψ) | |
2 | mtbid.maj | . . 3 ⊢ (φ → (ψ ↔ χ)) | |
3 | 2 | biimprd 214 | . 2 ⊢ (φ → (χ → ψ)) |
4 | 1, 3 | mtod 168 | 1 ⊢ (φ → ¬ χ) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 176 |
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 |
This theorem is referenced by: sylnib 295 eqneltrrd 2447 neleqtrd 2448 eueq3 3011 nnadjoinpw 4521 nnc3n3p2 6279 |
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