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Theorem a16nf 2004
Description: If dtru 4217 is false, then there is only one element in the universe, so 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 1907 . 2  |-  F/ z A. x  x  =  y
2 a16g 1898 . 2  |-  ( A. x  x  =  y  ->  ( ph  ->  A. z ph ) )
31, 2nfd 1758 1  |-  ( A. x  x  =  y  ->  F/ z ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1530   F/wnf 1534
This theorem is referenced by:  nfsb  2061  nfsbd  2063
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-nf 1535
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