Theorem nfiota 4343

Description: Bound-variable hypothesis builder for the ℩ class. (Contributed by NM, 23-Aug-2011.)

Hypothesis

Ref	Expression
nfiota.1	⊢ Ⅎxφ

Assertion

Ref	Expression
nfiota	⊢ Ⅎx(℩yφ)

Proof of Theorem nfiota

Step	Hyp	Ref	Expression
1		nftru 1554	. . 3 ⊢ Ⅎy ⊤
2		nfiota.1	. . . 4 ⊢ Ⅎxφ
3	2	a1i 10	. . 3 ⊢ ( ⊤ → Ⅎxφ)
4	1, 3	nfiotad 4342	. 2 ⊢ ( ⊤ → Ⅎx(℩yφ))
5	4	trud 1323	1 ⊢ Ⅎx(℩yφ)

Syntax hints:   ⊤ wtru 1316  Ⅎwnf 1544  Ⅎwnfc 2476  ℩cio 4337

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rex 2620  df-sn 3741  df-uni 3892  df-iota 4339

This theorem is referenced by:  csbiotag  4371  nffv  5334