Theorem nfbr 4091

Description: Bound-variable hypothesis builder for binary relation. (Contributed by NM, 1-Sep-1999.) (Revised by Mario Carneiro, 14-Oct-2016.)

Hypotheses

Ref	Expression
nfbr.1	|- F/_ x A
nfbr.2	|- F/_ x R
nfbr.3	|- F/_ x B

Assertion

Ref	Expression
nfbr	|- F/ x A R B

Proof of Theorem nfbr

Step	Hyp	Ref	Expression
1		nfbr.1	. . . 4 |- F/_ x A
2	1	a1i 9	. . 3 |- ( T. -> F/_ x A )
3		nfbr.2	. . . 4 |- F/_ x R
4	3	a1i 9	. . 3 |- ( T. -> F/_ x R )
5		nfbr.3	. . . 4 |- F/_ x B
6	5	a1i 9	. . 3 |- ( T. -> F/_ x B )
7	2, 4, 6	nfbrd 4090	. 2 |- ( T. -> F/ x A R B )
8	7	mptru 1382	1 |- F/ x A R B

Syntax hints:   T. wtru 1374   F/wnf 1483   F/_wnfc 2335   class class class wbr 4045

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-3an 983  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-v 2774  df-un 3170  df-sn 3639  df-pr 3640  df-op 3642  df-br 4046

This theorem is referenced by:  sbcbrg  4099  nfpo  4349  nfso  4350  pofun  4360  nfse  4389  nffrfor  4396  nfwe  4403  nfco  4844  nfcnv  4858  dfdmf  4872  dfrnf  4920  nfdm  4923  dffun6f  5285  dffun4f  5288  nffv  5588  funfvdm2f  5646  fvmptss2  5656  f1ompt  5733  fmptco  5748  nfiso  5877  nfofr  6167  ofrfval2  6177  tposoprab  6368  xpcomco  6923  nfsup  7096  caucvgprprlemaddq  7823  lble  9022  nfsum1  11700  nfsum  11701  fsum00  11806  mertenslem2  11880  nfcprod1  11898  nfcprod  11899  fprodap0  11965  fprodrec  11973  fproddivapf  11975  fprodap0f  11980  fprodle  11984  oddpwdclemdvds  12525  oddpwdclemndvds  12526