Theorem nfcsb1 3882

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 3881	. 2 ⊢ (⊤ → Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵)
4	3	mptru 1547	1 ⊢ Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵

Syntax hints:  ⊤wtru 1541  Ⅎwnfc 2876  ⦋csb 3859

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 2701

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 2708  df-cleq 2721  df-clel 2803  df-nfc 2878  df-sbc 3751  df-csb 3860

This theorem is referenced by:  nfcsb1v  3883  fsumsplit1  15687  iundisj  25482  disjabrex  32561  disjabrexf  32562  iundisjf  32568  iundisjfi  32769  rdgssun  37359  evl1gprodd  42098  disjinfi  45179  fsumsermpt  45570  climsubmpt  45651  climeldmeqmpt  45659  climfveqmpt  45662  climfveqmpt3  45673  climeldmeqmpt3  45680  climinf2mpt  45705  climinfmpt  45706  dvmptmulf  45928  dvnmptdivc  45929  sge0lempt  46401  sge0isummpt2  46423  meadjiun  46457  hoimbl2  46656  vonhoire  46663