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Theorem spesbc 3127
 Description: Existence form of spsbc 3058. (Contributed by Mario Carneiro, 18-Nov-2016.)
Assertion
Ref Expression
spesbc ([̣A / xφxφ)

Proof of Theorem spesbc
StepHypRef Expression
1 sbcex 3055 . . 3 ([̣A / xφA V)
2 rspesbca 3126 . . 3 ((A V A / xφ) → x V φ)
31, 2mpancom 650 . 2 ([̣A / xφx V φ)
4 rexv 2873 . 2 (x V φxφ)
53, 4sylib 188 1 ([̣A / xφxφ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∃wex 1541   ∈ wcel 1710  ∃wrex 2615  Vcvv 2859  [̣wsbc 3046 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rex 2620  df-v 2861  df-sbc 3047 This theorem is referenced by:  spesbcd  3128  opelopabsb  4697
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