Theorem nfcsb1 3852

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 3851	. 2 ⊢ (⊤ → Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵)
4	3	mptru 1546	1 ⊢ Ⅎ𝑥⦋𝐴 / 𝑥⦌𝐵

Syntax hints:  ⊤wtru 1540  Ⅎwnfc 2886  ⦋csb 3828

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-10 2139  ax-11 2156  ax-12 2173  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-tru 1542  df-ex 1784  df-nf 1788  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-nfc 2888  df-sbc 3712  df-csb 3829

This theorem is referenced by:  nfcsb1v  3853  fsumsplit1  15385  iundisj  24617  disjabrex  30822  disjabrexf  30823  iundisjf  30829  iundisjfi  31019  rdgssun  35476  disjinfi  42620  fsumsermpt  43010  climsubmpt  43091  climeldmeqmpt  43099  climfveqmpt  43102  climfveqmpt3  43113  climeldmeqmpt3  43120  climinf2mpt  43145  climinfmpt  43146  dvmptmulf  43368  dvnmptdivc  43369  sge0f1o  43810  sge0lempt  43838  sge0isummpt2  43860  meadjiun  43894  hoimbl2  44093  vonhoire  44100