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.

Step	Hyp	Ref	Expression
1		aev 1943	. 2
2		nfa1 1897	. . 3
3		axc16 1941	. . 3
4	2, 3	nfd 1878	. 2
5	1, 4	syl 16	1

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