Theorem rexlimivw 2423

Description: Weaker version of rexlimiv 2421. (Contributed by FL, 19-Sep-2011.)

Hypothesis

Ref	Expression
rexlimivw.1	⊢ (φ → ψ)

Assertion

Ref	Expression
rexlimivw	⊢ (∃x ∈ A φ → ψ)

Distinct variable group:   ψ,x

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

Proof of Theorem rexlimivw

Step	Hyp	Ref	Expression
1		rexlimivw.1	. . 3 ⊢ (φ → ψ)
2	1	a1i 9	. 2 ⊢ (x ∈ A → (φ → ψ))
3	2	rexlimiv 2421	1 ⊢ (∃x ∈ A φ → ψ)

Syntax hints:   → wi 4   ∈ wcel 1390  ∃wrex 2301

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-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-i5r 1425

This theorem depends on definitions:  df-bi 110  df-nf 1347  df-ral 2305  df-rex 2306

This theorem is referenced by:  r19.29vva  2450  eliun  3652  reusv3i  4157  elrnmptg  4529  fun11iun  5090  fmpt  5262  fliftfun  5379  elrnmpt2  5556  releldm2  5753  tfrlem4  5870  iinerm  6114  isfi  6177  ltbtwnnqq  6398  recexprlemlol  6598  recexprlemupu  6600