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Mirrors > Home > ILE Home > Th. List > a2i | GIF version |
Description: Inference derived from axiom ax-2 7. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
a2i.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
a2i | ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | a2i.1 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | ax-2 7 | . 2 ⊢ ((𝜑 → (𝜓 → 𝜒)) → ((𝜑 → 𝜓) → (𝜑 → 𝜒))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜒)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-2 7 |
This theorem is referenced by: imim2i 12 mpd 13 sylcom 28 pm2.43 53 ancl 316 ancr 319 anc2r 326 pm2.65 649 pm2.18dc 841 con4biddc 843 hbim1 1550 sbcof2 1783 ralimia 2496 ceqsalg 2717 rspct 2786 elabgt 2829 fvmptt 5520 ordiso2 6928 bj-exlimmp 13147 bj-rspgt 13164 bj-indint 13300 |
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