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Theorem a16nf 2135
Description: If dtru 4382 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 2042 . 2  |-  F/ z A. x  x  =  y
2 a16g 2048 . 2  |-  ( A. x  x  =  y  ->  ( ph  ->  A. z ph ) )
31, 2nfd 1782 1  |-  ( A. x  x  =  y  ->  F/ z ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1549   F/wnf 1553
This theorem is referenced by:  nfsb  2184  nfsbd  2186
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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