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Mirrors > Home > MPE Home > Th. List > 3adant3r2 | Structured version Visualization version GIF version |
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 17-Feb-2008.) |
Ref | Expression |
---|---|
ad4ant3.1 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
3adant3r2 | ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜏 ∧ 𝜒)) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ad4ant3.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) | |
2 | 1 | 3expb 1119 | . 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃) |
3 | 2 | 3adantr2 1169 | 1 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜏 ∧ 𝜒)) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 395 ∧ w3a 1086 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 207 df-an 396 df-3an 1088 |
This theorem is referenced by: plttr 18399 latjlej2 18511 latmlem1 18526 latmlem2 18527 latledi 18534 latmlej11 18535 latmlej12 18536 ipopos 18593 grppnpcan2 19064 mulgsubdir 19144 imasrng 20194 imasring 20343 isdomn4 20732 zntoslem 21592 mettri2 24366 mettri 24377 xmetrtri 24380 xmetrtri2 24381 metrtri 24382 ablomuldiv 30580 ablonnncan1 30585 nvmdi 30676 dipdi 30871 dipassr 30874 dipsubdir 30876 dipsubdi 30877 btwncomim 35994 cgr3tr4 36033 cgr3rflx 36035 colinbtwnle 36099 rngosubdi 37931 rngosubdir 37932 dmncan1 38062 dmncan2 38063 omlfh1N 39239 omlfh3N 39240 cvrnbtwn3 39257 cvrnbtwn4 39260 cvrcmp2 39265 hlatjrot 39354 cvrat3 39424 lplnribN 39533 ltrn2ateq 40162 dvalveclem 41007 mendlmod 43177 |
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