Theorem nfcsb1 3871

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 3870	. 2 ⊢ (⊤ → Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵)
4	3	mptru 1548	1 ⊢ Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵

Syntax hints:  ⊤wtru 1542  Ⅎwnfc 2877  ⦋csb 3848

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2112  ax-9 2120  ax-10 2143  ax-11 2159  ax-12 2179  ax-ext 2702

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1544  df-ex 1781  df-nf 1785  df-sb 2067  df-clab 2709  df-cleq 2722  df-clel 2804  df-nfc 2879  df-sbc 3740  df-csb 3849

This theorem is referenced by:  nfcsb1v  3872  fsumsplit1  15644  iundisj  25469  disjabrex  32552  disjabrexf  32553  iundisjf  32559  iundisjfi  32768  rdgssun  37391  evl1gprodd  42129  disjinfi  45208  fsumsermpt  45598  climsubmpt  45677  climeldmeqmpt  45685  climfveqmpt  45688  climfveqmpt3  45699  climeldmeqmpt3  45706  climinf2mpt  45731  climinfmpt  45732  dvmptmulf  45954  dvnmptdivc  45955  sge0lempt  46427  sge0isummpt2  46449  meadjiun  46483  hoimbl2  46682  vonhoire  46689