Theorem nfcsb1 3932

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 3931	. 2 ⊢ (⊤ → Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵)
4	3	mptru 1544	1 ⊢ Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵

Syntax hints:  ⊤wtru 1538  Ⅎwnfc 2888  ⦋csb 3908

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-10 2139  ax-11 2155  ax-12 2175  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-ex 1777  df-nf 1781  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-nfc 2890  df-sbc 3792  df-csb 3909

This theorem is referenced by:  nfcsb1v  3933  fsumsplit1  15778  iundisj  25597  disjabrex  32602  disjabrexf  32603  iundisjf  32609  iundisjfi  32804  rdgssun  37361  evl1gprodd  42099  disjinfi  45135  fsumsermpt  45535  climsubmpt  45616  climeldmeqmpt  45624  climfveqmpt  45627  climfveqmpt3  45638  climeldmeqmpt3  45645  climinf2mpt  45670  climinfmpt  45671  dvmptmulf  45893  dvnmptdivc  45894  sge0lempt  46366  sge0isummpt2  46388  meadjiun  46422  hoimbl2  46621  vonhoire  46628