Theorem r19.3rmv 3306

Description: Restricted quantification of wff not containing quantified variable. (Contributed by Jim Kingdon, 6-Aug-2018.)

Assertion

Ref	Expression
r19.3rmv	|- (E.y y e. A -> (ph <-> A.x e. A ph))

Distinct variable groups:   x,A   y,A   ph,x

Allowed substitution hint:   ph(y)

Proof of Theorem r19.3rmv

Step	Hyp	Ref	Expression
1		nfv 1418	. 2 |- F/xph
2	1	r19.3rm 3304	1 |- (E.y y e. A -> (ph <-> A.x e. A ph))

Syntax hints:   -> wi 4   <-> wb 98  E.wex 1378   e. wcel 1390  A.wral 2300

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019

This theorem depends on definitions:  df-bi 110  df-nf 1347  df-cleq 2030  df-clel 2033  df-ral 2305

This theorem is referenced by:  iinconstm  3657  cnvpom  4803  ssfiexmid  6254