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 1549	1 ⊢ Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵

Syntax hints:  ⊤wtru 1543  Ⅎwnfc 2884  ⦋csb 3838

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-10 2147  ax-11 2163  ax-12 2185  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1545  df-ex 1782  df-nf 1786  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-nfc 2886  df-sbc 3730  df-csb 3839

This theorem is referenced by:  nfcsb1v  3862  fsumsplit1  15707  iundisj  25515  disjabrex  32652  disjabrexf  32653  iundisjf  32659  iundisjfi  32869  rdgssun  37694  evl1gprodd  42556  disjinfi  45622  fsumsermpt  46009  climsubmpt  46088  climeldmeqmpt  46096  climfveqmpt  46099  climfveqmpt3  46110  climeldmeqmpt3  46117  climinf2mpt  46142  climinfmpt  46143  dvmptmulf  46365  dvnmptdivc  46366  sge0lempt  46838  sge0isummpt2  46860  meadjiun  46894  hoimbl2  47093  vonhoire  47100