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Theorem ssrexv 2999
 Description: Existential quantification restricted to a subclass. (Contributed by NM, 11-Jan-2007.)
Assertion
Ref Expression
ssrexv (AB → (x A φx B φ))
Distinct variable groups:   x,A   x,B
Allowed substitution hint:   φ(x)

Proof of Theorem ssrexv
StepHypRef Expression
1 ssel 2933 . . 3 (AB → (x Ax B))
21anim1d 319 . 2 (AB → ((x A φ) → (x B φ)))
32reximdv2 2412 1 (AB → (x A φx B φ))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∈ wcel 1390  ∃wrex 2301   ⊆ wss 2911 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-11 1394  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-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-rex 2306  df-in 2918  df-ss 2925 This theorem is referenced by:  iunss1  3659  moriotass  5439  lbzbi  8327  bj-nn0suc  9424
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