Theorem nfcsb1 3888

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 3887	. 2 ⊢ (⊤ → Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵)
4	3	mptru 1547	1 ⊢ Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵

Syntax hints:  ⊤wtru 1541  Ⅎwnfc 2877  ⦋csb 3865

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-10 2142  ax-11 2158  ax-12 2178  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-ex 1780  df-nf 1784  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-nfc 2879  df-sbc 3757  df-csb 3866

This theorem is referenced by:  nfcsb1v  3889  fsumsplit1  15718  iundisj  25456  disjabrex  32518  disjabrexf  32519  iundisjf  32525  iundisjfi  32726  rdgssun  37373  evl1gprodd  42112  disjinfi  45193  fsumsermpt  45584  climsubmpt  45665  climeldmeqmpt  45673  climfveqmpt  45676  climfveqmpt3  45687  climeldmeqmpt3  45694  climinf2mpt  45719  climinfmpt  45720  dvmptmulf  45942  dvnmptdivc  45943  sge0lempt  46415  sge0isummpt2  46437  meadjiun  46471  hoimbl2  46670  vonhoire  46677