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Mirrors > Home > NFE Home > Th. List > con4d | GIF version |
Description: Deduction derived from Axiom ax-3 8. (Contributed by NM, 26-Mar-1995.) |
Ref | Expression |
---|---|
con4d.1 | ⊢ (φ → (¬ ψ → ¬ χ)) |
Ref | Expression |
---|---|
con4d | ⊢ (φ → (χ → ψ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | con4d.1 | . 2 ⊢ (φ → (¬ ψ → ¬ χ)) | |
2 | ax-3 8 | . 2 ⊢ ((¬ ψ → ¬ χ) → (χ → ψ)) | |
3 | 1, 2 | syl 15 | 1 ⊢ (φ → (χ → ψ)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem is referenced by: pm2.21d 98 pm2.18 102 con2d 107 con1d 116 mt4d 130 impcon4bid 196 con4bid 284 exim 1575 sp 1747 spOLD 1748 axi11e 2332 necon2ad 2564 spc2gv 2942 spc3gv 2944 addceq0 6219 |
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