Mathbox for Stefan O'Rear < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  2sbcrex Unicode version

Theorem 2sbcrex 26187
 Description: Exchange an existential quantifier with two substitutions. (Contributed by Stefan O'Rear, 11-Oct-2014.)
Hypotheses
Ref Expression
2sbcrex.1
2sbcrex.2
Assertion
Ref Expression
2sbcrex
Distinct variable groups:   ,   ,   ,   ,   ,   ,
Allowed substitution hints:   (,,)   (,)   (,)   ()

Proof of Theorem 2sbcrex
StepHypRef Expression
1 2sbcrex.1 . . 3
2 2sbcrex.2 . . . . 5
3 sbcrexg 3142 . . . . 5
42, 3ax-mp 8 . . . 4
54sbcbiiOLD 3123 . . 3
61, 5ax-mp 8 . 2
7 sbcrexg 3142 . . 3
81, 7ax-mp 8 . 2
96, 8bitri 240 1
 Colors of variables: wff set class Syntax hints:   wb 176   wcel 1710  wrex 2620  cvv 2864  wsbc 3067 This theorem is referenced by:  2rexfrabdioph  26200  4rexfrabdioph  26202 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 1930  ax-ext 2339 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 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-ral 2624  df-rex 2625  df-v 2866  df-sbc 3068
 Copyright terms: Public domain W3C validator