Theorem nfiota 6462

Description: Bound-variable hypothesis builder for the ℩ class. Usage of this theorem is discouraged because it depends on ax-13 2377. Use the weaker nfiotaw 6460 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 1806	. . 3 ⊢ Ⅎ𝑦⊤
2		nfiota.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3	2	a1i 11	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
4	1, 3	nfiotad 6461	. 2 ⊢ (⊤ → Ⅎ𝑥(℩𝑦𝜑))
5	4	mptru 1549	1 ⊢ Ⅎ𝑥(℩𝑦𝜑)

Syntax hints:  ⊤wtru 1543  Ⅎwnf 1785  Ⅎwnfc 2884  ℩cio 6454

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-10 2147  ax-11 2163  ax-12 2185  ax-13 2377  ax-ext 2709

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1545  df-ex 1782  df-nf 1786  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-nfc 2886  df-ral 3053  df-rex 3063  df-v 3444  df-ss 3920  df-sn 4583  df-uni 4866  df-iota 6456

This theorem is referenced by: (None)