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Theorem nfop 4604
 Description: Bound-variable hypothesis builder for ordered pairs. (Contributed by SF, 2-Jan-2015.)
Hypotheses
Ref Expression
nfop.1
nfop.2
Assertion
Ref Expression
nfop

Proof of Theorem nfop
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-op 4566 . 2 Phi Phi 0c
2 nfop.1 . . . . 5
3 nfv 1619 . . . . 5 Phi
42, 3nfrex 2669 . . . 4 Phi
54nfab 2493 . . 3 Phi
6 nfop.2 . . . . 5
7 nfv 1619 . . . . 5 Phi 0c
86, 7nfrex 2669 . . . 4 Phi 0c
98nfab 2493 . . 3 Phi 0c
105, 9nfun 3231 . 2 Phi Phi 0c
111, 10nfcxfr 2486 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1642  cab 2339  wnfc 2476  wrex 2615   cun 3207  csn 3737  0cc0c 4374  cop 4561   Phi cphi 4562 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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-nan 1288  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-ral 2619  df-rex 2620  df-nin 3211  df-compl 3212  df-un 3214  df-op 4566 This theorem is referenced by:  nfopd  4605
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