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Theorem moxfr 26733
 Description: Transfer at-most-one between related expressions. (Contributed by Stefan O'Rear, 12-Feb-2015.)
Hypotheses
Ref Expression
moxfr.a
moxfr.b
moxfr.c
Assertion
Ref Expression
moxfr
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem moxfr
StepHypRef Expression
1 moxfr.a . . . . . 6
21a1i 11 . . . . 5
3 moxfr.b . . . . . . . 8
4 euex 2304 . . . . . . . 8
53, 4ax-mp 8 . . . . . . 7
6 rexv 2970 . . . . . . 7
75, 6mpbir 201 . . . . . 6
87a1i 11 . . . . 5
9 moxfr.c . . . . 5
102, 8, 9rexxfr 4743 . . . 4
11 rexv 2970 . . . 4
12 rexv 2970 . . . 4
1310, 11, 123bitr3i 267 . . 3
141, 3, 9euxfr 3120 . . 3
1513, 14imbi12i 317 . 2
16 df-mo 2286 . 2
17 df-mo 2286 . 2
1815, 16, 173bitr4i 269 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wex 1550   wceq 1652   wcel 1725  weu 2281  wmo 2282  wrex 2706  cvv 2956 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-v 2958
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