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Theorem moxfr 35452
 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 2290 . . . . . . . 8
53, 4ax-mp 5 . . . . . . 7
6 rexv 3096 . . . . . . 7
75, 6mpbir 212 . . . . . 6
87a1i 11 . . . . 5
9 moxfr.c . . . . 5
102, 8, 9rexxfr 4637 . . . 4
11 rexv 3096 . . . 4
12 rexv 3096 . . . 4
1310, 11, 123bitr3i 278 . . 3
141, 3, 9euxfr 3257 . . 3
1513, 14imbi12i 327 . 2
16 df-mo 2270 . 2
17 df-mo 2270 . 2
1815, 16, 173bitr4i 280 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wceq 1437  wex 1659   wcel 1868  weu 2265  wmo 2266  wrex 2776  cvv 3081 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-eu 2269  df-mo 2270  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2572  df-ral 2780  df-rex 2781  df-v 3083 This theorem is referenced by: (None)
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