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Theorem mosubop 4457
 Description: "At most one" remains true inside ordered pair quantification. (Contributed by NM, 28-May-1995.)
Hypothesis
Ref Expression
mosubop.1
Assertion
Ref Expression
mosubop
Distinct variable group:   ,,,
Allowed substitution hints:   (,,)

Proof of Theorem mosubop
StepHypRef Expression
1 mosubop.1 . . 3
21gen2 1557 . 2
3 mosubopt 4456 . 2
42, 3ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wa 360  wal 1550  wex 1551   wceq 1653  wmo 2284  cop 3819 This theorem is referenced by:  oprabex3  6190  ov3  6212  ov6g  6213  axaddf  9022  axmulf  9023 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825
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