Theorem nfmod 2037

Description: Bound-variable hypothesis builder for "at most one". (Contributed by Mario Carneiro, 14-Nov-2016.)

Hypotheses

Ref	Expression
nfeud.1	|- F/ y ph
nfeud.2	|- ( ph -> F/ x ps )

Assertion

Ref	Expression
nfmod	|- ( ph -> F/ x E* y ps )

Proof of Theorem nfmod

Step	Hyp	Ref	Expression
1		df-mo 2024	. 2 |- ( E* y ps <-> ( E. y ps -> E! y ps ) )
2		nfeud.1	. . . 4 |- F/ y ph
3		nfeud.2	. . . 4 |- ( ph -> F/ x ps )
4	2, 3	nfexd 1755	. . 3 |- ( ph -> F/ x E. y ps )
5	2, 3	nfeud 2036	. . 3 |- ( ph -> F/ x E! y ps )
6	4, 5	nfimd 1579	. 2 |- ( ph -> F/ x ( E. y ps -> E! y ps ) )
7	1, 6	nfxfrd 1469	1 |- ( ph -> F/ x E* y ps )

Syntax hints:   -> wi 4   F/wnf 1454   E.wex 1486   E!weu 2020   E*wmo 2021

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 705  ax-5 1441  ax-7 1442  ax-gen 1443  ax-ie1 1487  ax-ie2 1488  ax-8 1498  ax-10 1499  ax-11 1500  ax-i12 1501  ax-bndl 1503  ax-4 1504  ax-17 1520  ax-i9 1524  ax-ial 1528  ax-i5r 1529

This theorem depends on definitions:  df-bi 116  df-tru 1352  df-nf 1455  df-sb 1757  df-eu 2023  df-mo 2024

This theorem is referenced by:  nfmo  2040