Theorem eximdv 1852

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 1506	. 2 ⊢ (𝜑 → ∀𝑥𝜑)
2		alimdv.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
3	1, 2	eximdh 1590	1 ⊢ (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))

Syntax hints:   → wi 4  ∃wex 1468

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-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  2eximdv  1854  reximdv2  2531  cgsexg  2721  spc3egv  2777  euind  2871  ssel  3091  reupick  3360  reximdva0m  3378  uniss  3757  eusvnfb  4375  coss1  4694  coss2  4695  dmss  4738  dmcosseq  4810  funssres  5165  imain  5205  brprcneu  5414  fv3  5444  dffo4  5568  dffo5  5569  f1eqcocnv  5692  mapsn  6584  ctssdccl  6996  acfun  7063  ccfunen  7079  dmaddpq  7187  dmmulpq  7188  recexprlemlol  7434  recexprlemupu  7436  ioom  10038  ctinfom  11941  ctinf  11943  txcn  12444