Theorem nfcsb1 3029

Description: Bound-variable hypothesis builder for substitution into a class. (Contributed by Mario Carneiro, 12-Oct-2016.)

Hypothesis

Ref	Expression
nfcsb1.1	|- F/_ x A

Assertion

Ref	Expression
nfcsb1	|- F/_ x [_ A / x ]_ B

Proof of Theorem nfcsb1

Step	Hyp	Ref	Expression
1		nfcsb1.1	. . . 4 |- F/_ x A
2	1	a1i 9	. . 3 |- ( T. -> F/_ x A )
3	2	nfcsb1d 3028	. 2 |- ( T. -> F/_ x [_ A / x ]_ B )
4	3	mptru 1340	1 |- F/_ x [_ A / x ]_ B

Syntax hints:   T. wtru 1332   F/_wnfc 2266   [_csb 2998

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-sbc 2905  df-csb 2999

This theorem is referenced by:  nfcsb1v  3030