Theorem nfae 1954

Description: All variables are effectively bound in an identical variable specifier. (Contributed by Mario Carneiro, 11-Aug-2016.)

Assertion

Ref	Expression
nfae	⊢ Ⅎz∀x x = y

Proof of Theorem nfae

Step	Hyp	Ref	Expression
1		hbae 1953	. 2 ⊢ (∀x x = y → ∀z∀x x = y)
2	1	nfi 1551	1 ⊢ Ⅎz∀x x = y

Syntax hints:  ∀wal 1540  Ⅎwnf 1544

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545

This theorem is referenced by:  nfnae  1956  sbequ5  2031  a16nf  2051  sbcom  2089  sbcom2  2114  exists1  2293  copsexg  4608