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Theorem ssrmo 23934
 Description: "At most one" existential quantification restricted to a subclass. (Contributed by Thierry Arnoux, 8-Oct-2017.)
Hypotheses
Ref Expression
ssrmo.1
ssrmo.2
Assertion
Ref Expression
ssrmo

Proof of Theorem ssrmo
StepHypRef Expression
1 ssrmo.1 . . . . 5
2 ssrmo.2 . . . . 5
31, 2dfss2f 3299 . . . 4
43biimpi 187 . . 3
5 pm3.45 808 . . . 4
65alimi 1565 . . 3
7 moim 2300 . . 3
84, 6, 73syl 19 . 2
9 df-rmo 2674 . 2
10 df-rmo 2674 . 2
118, 9, 103imtr4g 262 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359  wal 1546   wcel 1721  wmo 2255  wnfc 2527  wrmo 2669   wss 3280 This theorem is referenced by:  disjss1f  23969 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2258  df-mo 2259  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-rmo 2674  df-in 3287  df-ss 3294
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