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Theorem rspsbc2 32259
 Description: rspsbc 3414 with two quantifying variables. This proof is rspsbc2VD 32610 automatically translated and minimized. (Contributed by Alan Sare, 31-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
rspsbc2
Distinct variable groups:   ,   ,   ,,
Allowed substitution hints:   (,)   ()   ()   (,)

Proof of Theorem rspsbc2
StepHypRef Expression
1 idd 24 . 2
2 rspsbc 3414 . . . 4
32a1d 25 . . 3
4 sbcralg 3408 . . . 4
54biimpd 207 . . 3
63, 5syl6d 69 . 2
7 rspsbc 3414 . 2
81, 6, 7syl10 73 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wcel 1762  wral 2807  wsbc 3324 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 970  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2446  df-cleq 2452  df-clel 2455  df-nfc 2610  df-ral 2812  df-v 3108  df-sbc 3325 This theorem is referenced by:  tratrb  32261  tratrbVD  32616
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