Theorem nfbr 4050

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 4049	. 2 |- ( T. -> F/ x A R B )
8	7	mptru 1362	1 |- F/ x A R B

Syntax hints:   T. wtru 1354   F/wnf 1460   F/_wnfc 2306   class class class wbr 4004

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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2740  df-un 3134  df-sn 3599  df-pr 3600  df-op 3602  df-br 4005

This theorem is referenced by:  sbcbrg  4058  nfpo  4302  nfso  4303  pofun  4313  nfse  4342  nffrfor  4349  nfwe  4356  nfco  4793  nfcnv  4807  dfdmf  4821  dfrnf  4869  nfdm  4872  dffun6f  5230  dffun4f  5233  nffv  5526  funfvdm2f  5582  fvmptss2  5592  f1ompt  5668  fmptco  5683  nfiso  5807  nfofr  6089  ofrfval2  6099  tposoprab  6281  xpcomco  6826  nfsup  6991  caucvgprprlemaddq  7707  lble  8904  nfsum1  11364  nfsum  11365  fsum00  11470  mertenslem2  11544  nfcprod1  11562  nfcprod  11563  fprodap0  11629  fprodrec  11637  fproddivapf  11639  fprodap0f  11644  fprodle  11648  oddpwdclemdvds  12170  oddpwdclemndvds  12171