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Mirrors > Home > NFE Home > Th. List > mtbird | GIF version |
Description: A deduction from a biconditional, similar to modus tollens. (Contributed by NM, 10-May-1994.) |
Ref | Expression |
---|---|
mtbird.min | ⊢ (φ → ¬ χ) |
mtbird.maj | ⊢ (φ → (ψ ↔ χ)) |
Ref | Expression |
---|---|
mtbird | ⊢ (φ → ¬ ψ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mtbird.min | . 2 ⊢ (φ → ¬ χ) | |
2 | mtbird.maj | . . 3 ⊢ (φ → (ψ ↔ χ)) | |
3 | 2 | biimpd 198 | . 2 ⊢ (φ → (ψ → χ)) |
4 | 1, 3 | mtod 168 | 1 ⊢ (φ → ¬ ψ) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 176 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 |
This theorem depends on definitions: df-bi 177 |
This theorem is referenced by: eqneltrd 2446 neleqtrrd 2449 ltfinirr 4457 nnadjoin 4520 vfin1cltv 4547 fvun1 5379 nnc3n3p1 6278 nnc3p1n3p2 6280 nchoicelem1 6289 nchoicelem2 6290 nchoicelem14 6302 |
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