Theorem rexlimivw 2621

Description: Weaker version of rexlimiv 2619. (Contributed by FL, 19-Sep-2011.)

Hypothesis

Ref	Expression
rexlimivw.1	|- ( ph -> ps )

Assertion

Ref	Expression
rexlimivw	|- ( E. x e. A ph -> ps )

Distinct variable group:   ps, x

Allowed substitution hints:   ph( x)   A( x)

Proof of Theorem rexlimivw

Step	Hyp	Ref	Expression
1		rexlimivw.1	. . 3 |- ( ph -> ps )
2	1	a1i 9	. 2 |- ( x e. A -> ( ph -> ps ) )
3	2	rexlimiv 2619	1 |- ( E. x e. A ph -> ps )

Syntax hints:   -> wi 4   e. wcel 2178   E.wrex 2487

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1471  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-4 1534  ax-17 1550  ax-ial 1558  ax-i5r 1559

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-ral 2491  df-rex 2492

This theorem is referenced by:  r19.29vva  2653  eliun  3945  reusv3i  4524  elrnmptg  4949  fun11iun  5565  fmpt  5753  fliftfun  5888  elrnmpo  6082  releldm2  6294  tfrlem4  6422  iinerm  6717  elixpsn  6845  isfi  6875  cardcl  7314  cardval3ex  7318  ltbtwnnqq  7563  recexprlemlol  7774  recexprlemupu  7776  suplocsr  7957  restsspw  13196  rhmdvdsr  14052  ssnei  14738  tgcnp  14796  xmetunirn  14945  metss  15081  metrest  15093