Theorem a16nf 1838

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

Step	Hyp	Ref	Expression
1		nfae 1697	. 2 |- F/ z A. x x = y
2		a16g 1836	. 2 |- ( A. x x = y -> ( ph -> A. z ph ) )
3	1, 2	nfd 1503	1 |- ( A. x x = y -> F/ z ph )

Syntax hints:   -> wi 4   A.wal 1329   F/wnf 1436

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514

This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736

This theorem is referenced by:  nfsbxy  1913  nfsbxyt  1914  dvelimor  1991