Theorem nfiota 6379

Description: Bound-variable hypothesis builder for the ℩ class. Usage of this theorem is discouraged because it depends on ax-13 2373. Use the weaker nfiotaw 6377 when possible. (Contributed by NM, 23-Aug-2011.) (New usage is discouraged.)

Hypothesis

Ref	Expression
nfiota.1	⊢ Ⅎ𝑥𝜑

Assertion

Ref	Expression
nfiota	⊢ Ⅎ𝑥(℩𝑦𝜑)

Proof of Theorem nfiota

Step	Hyp	Ref	Expression
1		nftru 1812	. . 3 ⊢ Ⅎ𝑦⊤
2		nfiota.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3	2	a1i 11	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
4	1, 3	nfiotad 6378	. 2 ⊢ (⊤ → Ⅎ𝑥(℩𝑦𝜑))
5	4	mptru 1550	1 ⊢ Ⅎ𝑥(℩𝑦𝜑)

Syntax hints:  ⊤wtru 1544  Ⅎwnf 1791  Ⅎwnfc 2887  ℩cio 6371

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2114  ax-9 2122  ax-10 2143  ax-11 2160  ax-12 2177  ax-13 2373  ax-ext 2710

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 848  df-tru 1546  df-ex 1788  df-nf 1792  df-sb 2073  df-clab 2717  df-cleq 2731  df-clel 2818  df-nfc 2889  df-ral 3069  df-rex 3070  df-v 3425  df-in 3891  df-ss 3901  df-sn 4559  df-uni 4837  df-iota 6373

This theorem is referenced by:  nfsumOLD  15306