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Theorem ax16nf 1944
Description: If dtru 4643 is false, then there is only one element in the universe, so everything satisfies F/. (Contributed by Mario Carneiro, 7-Oct-2016.) Remove dependency on ax-11 1842. (Revised by Wolf Lammen, 9-Sep-2018.) (Proof shortened by BJ, 14-Jun-2019.)
Assertion
Ref Expression
ax16nf
Distinct variable group:   ,

Proof of Theorem ax16nf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 aev 1943 . 2
2 nfa1 1897 . . 3
3 axc16 1941 . . 3
42, 3nfd 1878 . 2
51, 4syl 16 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  A.wal 1393  F/wnf 1616
This theorem is referenced by:  nfsb  2184  nfsbd  2186
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854
This theorem depends on definitions:  df-bi 185  df-ex 1613  df-nf 1617
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