Theorem nfcsb1 3897

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 3896	. 2 ⊢ (⊤ → Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵)
4	3	mptru 1547	1 ⊢ Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵

Syntax hints:  ⊤wtru 1541  Ⅎwnfc 2883  ⦋csb 3874

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 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-11 2157  ax-12 2177  ax-ext 2707

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 2065  df-clab 2714  df-cleq 2727  df-clel 2809  df-nfc 2885  df-sbc 3766  df-csb 3875

This theorem is referenced by:  nfcsb1v  3898  fsumsplit1  15761  iundisj  25501  disjabrex  32563  disjabrexf  32564  iundisjf  32570  iundisjfi  32773  rdgssun  37396  evl1gprodd  42130  disjinfi  45216  fsumsermpt  45608  climsubmpt  45689  climeldmeqmpt  45697  climfveqmpt  45700  climfveqmpt3  45711  climeldmeqmpt3  45718  climinf2mpt  45743  climinfmpt  45744  dvmptmulf  45966  dvnmptdivc  45967  sge0lempt  46439  sge0isummpt2  46461  meadjiun  46495  hoimbl2  46694  vonhoire  46701