Theorem eximdv 1880

Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 27-Apr-1994.)

Hypothesis

Ref	Expression
alimdv.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
eximdv	⊢ (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))

Distinct variable group:   𝜑,𝑥

Allowed substitution hints:   𝜓(𝑥)   𝜒(𝑥)

Proof of Theorem eximdv

Step	Hyp	Ref	Expression
1		ax-17 1526	. 2 ⊢ (𝜑 → ∀𝑥𝜑)
2		alimdv.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
3	1, 2	eximdh 1611	1 ⊢ (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))

Syntax hints:   → wi 4  ∃wex 1492

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 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-17 1526  ax-ial 1534

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  2eximdv  1882  reximdv2  2576  cgsexg  2772  spc3egv  2829  euind  2924  ssel  3149  reupick  3419  reximdva0m  3438  uniss  3830  eusvnfb  4454  coss1  4782  coss2  4783  dmss  4826  dmcosseq  4898  funssres  5258  imain  5298  brprcneu  5508  fv3  5538  dffo4  5664  dffo5  5665  f1eqcocnv  5791  mapsn  6689  ctssdccl  7109  acfun  7205  ccfunen  7262  cc4f  7267  cc4n  7269  dmaddpq  7377  dmmulpq  7378  recexprlemlol  7624  recexprlemupu  7626  ioom  10258  ctinfom  12423  ctinf  12425  omctfn  12438  nninfdclemp1  12445  subgintm  13011  txcn  13668