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Mirrors > Home > MPE Home > Th. List > pm2.61d2 | Structured version Visualization version GIF version |
Description: Inference eliminating an antecedent. (Contributed by NM, 18-Aug-1993.) |
Ref | Expression |
---|---|
pm2.61d2.1 | ⊢ (𝜑 → (¬ 𝜓 → 𝜒)) |
pm2.61d2.2 | ⊢ (𝜓 → 𝜒) |
Ref | Expression |
---|---|
pm2.61d2 | ⊢ (𝜑 → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.61d2.2 | . . 3 ⊢ (𝜓 → 𝜒) | |
2 | 1 | a1i 11 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) |
3 | pm2.61d2.1 | . 2 ⊢ (𝜑 → (¬ 𝜓 → 𝜒)) | |
4 | 2, 3 | pm2.61d 169 | 1 ⊢ (𝜑 → 𝜒) |
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: pm2.61ii 176 jaoi 393 nfald2 2319 nfsbd 2430 2ax6elem 2437 sbal1 2448 sbal2 2449 nfabd2 2770 rgen2a 2960 posn 5110 frsn 5112 relimasn 5407 nfriotad 6519 tfinds 6951 curry1val 7157 curry2val 7161 onfununi 7325 findcard2s 8086 xpfi 8116 fiint 8122 acndom 8757 dfac12k 8852 iundom2g 9241 nqereu 9630 ltapr 9746 xrmax1 11880 xrmin2 11883 max1ALT 11891 hasheq0 13015 swrdnd2 13285 cshw1 13419 bezout 15098 ptbasfi 21194 filcon 21497 pcopt 22630 ioorinv 23150 itg1addlem2 23270 itg1addlem4 23272 itgss 23384 bddmulibl 23411 wlkdvspthlem 26137 mdsymlem6 28651 sumdmdlem2 28662 bj-ax6elem1 31840 wl-equsb4 32517 wl-sbalnae 32524 poimirlem13 32592 poimirlem25 32604 poimirlem27 32606 sgoldbaltlem1 40201 pthdlem2 40974 setrec2fun 42238 |
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