Theorem nfcsb1 3861

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

Hypothesis

Ref	Expression
nfcsb1.1	⊢ Ⅎ𝑥𝐴

Assertion

Ref	Expression
nfcsb1	⊢ Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵

Proof of Theorem nfcsb1

Step	Hyp	Ref	Expression
1		nfcsb1.1	. . . 4 ⊢ Ⅎ𝑥𝐴
2	1	a1i 11	. . 3 ⊢ (⊤ → Ⅎ𝑥𝐴)
3	2	nfcsb1d 3860	. 2 ⊢ (⊤ → Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵)
4	3	mptru 1554	1 ⊢ Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵

Syntax hints:  ⊤wtru 1548  Ⅎwnfc 2887  ⦋csb 3838

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-10 2152  ax-11 2168  ax-12 2189  ax-ext 2712

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-tru 1550  df-ex 1787  df-nf 1791  df-sb 2074  df-clab 2719  df-cleq 2732  df-clel 2815  df-nfc 2889  df-sbc 3731  df-csb 3839

This theorem is referenced by:  nfcsb1v  3862  fsumsplit1  15705  iundisj  25540  disjabrex  32678  disjabrexf  32679  iundisjf  32685  iundisjfi  32895  rdgssun  37741  evl1gprodd  42603  disjinfi  45640  fsumsermpt  46025  climsubmpt  46104  climeldmeqmpt  46112  climfveqmpt  46115  climfveqmpt3  46126  climeldmeqmpt3  46133  climinf2mpt  46158  climinfmpt  46159  dvmptmulf  46381  dvnmptdivc  46382  sge0lempt  46854  sge0isummpt2  46876  meadjiun  46910  hoimbl2  47109  vonhoire  47116