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Theorem moim 1961
Description: "At most one" is preserved through implication (notice wff reversal). (Contributed by NM, 22-Apr-1995.)
Assertion
Ref Expression
moim

Proof of Theorem moim
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfa1 1431 . . 3  F/
2 ax-4 1397 . . . . . 6
3 spsbim 1721 . . . . . 6
42, 3anim12d 318 . . . . 5
54imim1d 69 . . . 4
65alimdv 1756 . . 3
71, 6alimd 1411 . 2
8 ax-17 1416 . . 3
98mo3h 1950 . 2
10 ax-17 1416 . . 3
1110mo3h 1950 . 2
127, 9, 113imtr4g 194 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97  wal 1240  wsb 1642  wmo 1898
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-eu 1900  df-mo 1901
This theorem is referenced by:  moimi  1962  euimmo  1964  moexexdc  1981  euexex  1982  rmoim  2734  rmoimi2  2736  disjss1  3742  reusv1  4156  funmo  4860
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