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Mirrors > Home > MPE Home > Th. List > imim2i | Structured version Visualization version GIF version |
Description: Inference adding common antecedents in an implication. Inference associated with imim2 58. Its associated inference is syl 17. (Contributed by NM, 28-Dec-1992.) |
Ref | Expression |
---|---|
imim2i.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
imim2i | ⊢ ((𝜒 → 𝜑) → (𝜒 → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imim2i.1 | . . 3 ⊢ (𝜑 → 𝜓) | |
2 | 1 | a1i 11 | . 2 ⊢ (𝜒 → (𝜑 → 𝜓)) |
3 | 2 | a2i 14 | 1 ⊢ ((𝜒 → 𝜑) → (𝜒 → 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 |
This theorem is referenced by: imim12i 62 imim3i 64 ja 186 imim21b 396 jcab 519 pm3.48 963 nanass 1509 nic-ax 1676 nic-axALT 1677 tbw-bijust 1701 merco1 1716 19.23v 1946 19.24 1990 hbsbw 2170 sb4a 2480 2eu6 2653 axi5r 2696 ralrexbidOLD 3108 r19.36v 3184 ceqsal1t 3505 vtoclgft 3541 spcgft 3579 elabgt 3663 mo2icl 3711 euind 3721 reu6 3723 reuind 3750 sbciegft 3816 elpwunsn 4688 dfiin2g 5036 invdisj 5133 ssrel 5783 ssrelOLD 5784 dff3 7102 fnoprabg 7531 tfindsg 7850 findsg 7890 zfrep6 7941 tz7.48-1 8443 odi 8579 r1sdom 9769 kmlem6 10150 kmlem12 10156 zorng 10499 squeeze0 12117 xrsupexmnf 13284 xrinfmexpnf 13285 mptnn0fsuppd 13963 rexanre 15293 pmatcollpw2lem 22279 tgcnp 22757 lmcvg 22766 iblcnlem 25306 limcresi 25402 isch3 30525 disjexc 31855 cntmeas 33255 bnj900 33971 bnj1172 34043 bnj1174 34045 bnj1176 34047 gonarlem 34416 goalrlem 34418 axextdfeq 34800 hbimtg 34809 nn0prpw 35256 meran3 35346 waj-ax 35347 lukshef-ax2 35348 imsym1 35351 bj-peircestab 35477 bj-orim2 35480 bj-andnotim 35514 bj-ssbid2ALT 35588 bj-19.21bit 35616 bj-substax12 35647 bj-ceqsalt0 35812 bj-ceqsalt1 35813 wl-embant 36427 contrd 37013 ax12indi 37862 ltrnnid 39055 ismrc 41487 frege55lem1a 42665 frege55lem1b 42694 frege55lem1c 42715 frege92 42754 pm11.71 43204 exbir 43287 ax6e2ndeqVD 43718 ax6e2ndeqALT 43740 r19.36vf 43873 nn0sumshdiglemA 47353 nn0sumshdiglemB 47354 setrec2mpt 47790 |
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