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Theorem mosub 2719
Description: "At most one" remains true after substitution. (Contributed by NM, 9-Mar-1995.)
Hypothesis
Ref Expression
mosub.1  |-  E* x ph
Assertion
Ref Expression
mosub  |-  E* x E. y ( y  =  A  /\  ph )
Distinct variable group:    x, y, A
Allowed substitution hints:    ph( x, y)

Proof of Theorem mosub
StepHypRef Expression
1 mosubt 2718 . 2  |-  ( A. y E* x ph  ->  E* x E. y ( y  =  A  /\  ph ) )
2 mosub.1 . 2  |-  E* x ph
31, 2mpg 1340 1  |-  E* x E. y ( y  =  A  /\  ph )
Colors of variables: wff set class
Syntax hints:    /\ wa 97    = wceq 1243   E.wex 1381   E*wmo 1901
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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-clab 2027  df-cleq 2033  df-clel 2036  df-v 2559
This theorem is referenced by: (None)
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