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Theorem bm1.1 2338
Description: Any set defined by a property is the only set defined by that property. Theorem 1.1 of [BellMachover] p. 462. (Contributed by NM, 30-Jun-1994.)
Hypothesis
Ref Expression
bm1.1.1  F/
Assertion
Ref Expression
bm1.1
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem bm1.1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1619 . . . . . . . 8  F/
2 bm1.1.1 . . . . . . . 8  F/
31, 2nfbi 1834 . . . . . . 7  F/
43nfal 1842 . . . . . 6  F/
5 elequ2 1715 . . . . . . . 8
65bibi1d 310 . . . . . . 7
76albidv 1625 . . . . . 6
84, 7sbie 2038 . . . . 5
9 19.26 1593 . . . . . 6
10 biantr 897 . . . . . . . 8
1110alimi 1559 . . . . . . 7
12 ax-ext 2334 . . . . . . 7
1311, 12syl 15 . . . . . 6
149, 13sylbir 204 . . . . 5
158, 14sylan2b 461 . . . 4
1615gen2 1547 . . 3
1716jctr 526 . 2
18 nfv 1619 . . 3  F/
1918eu2 2229 . 2
2017, 19sylibr 203 1
Colors of variables: wff set class
Syntax hints:   wi 4   wb 176   wa 358  wal 1540  wex 1541   F/wnf 1544   wceq 1642  wsb 1648   wcel 1710  weu 2204
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-14 1714  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-eu 2208
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