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Theorem nfmpt2 5675
 Description: Bound-variable hypothesis builder for the maps-to notation. (Contributed by NM, 20-Feb-2013.)
Hypotheses
Ref Expression
nfmpt2.1 zA
nfmpt2.2 zB
nfmpt2.3 zC
Assertion
Ref Expression
nfmpt2 z(x A, y B C)
Distinct variable groups:   x,z   y,z
Allowed substitution hints:   A(x,y,z)   B(x,y,z)   C(x,y,z)

Proof of Theorem nfmpt2
Dummy variable w is distinct from all other variables.
StepHypRef Expression
1 df-mpt2 5654 . 2 (x A, y B C) = {x, y, w ((x A y B) w = C)}
2 nfmpt2.1 . . . . . 6 zA
32nfcri 2483 . . . . 5 z x A
4 nfmpt2.2 . . . . . 6 zB
54nfcri 2483 . . . . 5 z y B
63, 5nfan 1824 . . . 4 z(x A y B)
7 nfmpt2.3 . . . . 5 zC
87nfeq2 2500 . . . 4 z w = C
96, 8nfan 1824 . . 3 z((x A y B) w = C)
109nfoprab 5549 . 2 z{x, y, w ((x A y B) w = C)}
111, 10nfcxfr 2486 1 z(x A, y B C)
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 358   = wceq 1642   ∈ wcel 1710  Ⅎwnfc 2476  {coprab 5527   ↦ cmpt2 5653 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 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-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-oprab 5528  df-mpt2 5654 This theorem is referenced by: (None)
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