Theorem nfiota 6454

Description: Bound-variable hypothesis builder for the ℩ class. Usage of this theorem is discouraged because it depends on ax-13 2380. Use the weaker nfiotaw 6452 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 1811	. . 3 ⊢ Ⅎ𝑦⊤
2		nfiota.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3	2	a1i 11	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
4	1, 3	nfiotad 6453	. 2 ⊢ (⊤ → Ⅎ𝑥(℩𝑦𝜑))
5	4	mptru 1554	1 ⊢ Ⅎ𝑥(℩𝑦𝜑)

Syntax hints:  ⊤wtru 1548  Ⅎwnf 1790  Ⅎwnfc 2887  ℩cio 6446

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-10 2152  ax-11 2168  ax-12 2189  ax-13 2380  ax-ext 2712

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-tru 1550  df-ex 1787  df-nf 1791  df-sb 2074  df-clab 2719  df-cleq 2732  df-clel 2815  df-nfc 2889  df-ral 3055  df-rex 3065  df-v 3434  df-ss 3907  df-sn 4563  df-uni 4846  df-iota 6448

This theorem is referenced by: (None)