Theorem nfcsb1 3548

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 11	. . 3 |- ( T. -> F/_ x A )
3	2	nfcsb1d 3547	. 2 |- ( T. -> F/_ x [_ A / x ]_ B )
4	3	trud 1493	1 |- F/_ x [_ A / x ]_ B

Syntax hints:   T. wtru 1484   F/_wnfc 2751   [_csb 3533

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-sbc 3436  df-csb 3534

This theorem is referenced by:  nfcsb1v  3549  fprodsplit1f  14721  iundisj  23316  disjabrex  29395  disjabrexf  29396  iundisjf  29402  iundisjfi  29555  disjinfi  39380  fsumsplit1  39804  fsumsermpt  39811  climsubmpt  39892  climeldmeqmpt  39900  climfveqmpt  39903  climfveqmpt3  39914  climeldmeqmpt3  39921  climinf2mpt  39946  climinfmpt  39947  dvmptmulf  40152  dvnmptdivc  40153  sge0f1o  40599  sge0lempt  40627  sge0isummpt2  40649  meadjiun  40683  hoimbl2  40879  vonhoire  40886