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Theorem a16nf 1866
Description: If there is only one element in the universe, then everything satisfies  F/. (Contributed by Mario Carneiro, 7-Oct-2016.)
Assertion
Ref Expression
a16nf  |-  ( A. x  x  =  y  ->  F/ z ph )
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y, z)

Proof of Theorem a16nf
StepHypRef Expression
1 nfae 1719 . 2  |-  F/ z A. x  x  =  y
2 a16g 1864 . 2  |-  ( A. x  x  =  y  ->  ( ph  ->  A. z ph ) )
31, 2nfd 1523 1  |-  ( A. x  x  =  y  ->  F/ z ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1351   F/wnf 1460
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763
This theorem is referenced by:  nfsbxy  1942  nfsbxyt  1943  dvelimor  2018
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