Theorem nfiota 6322

Description: Bound-variable hypothesis builder for the ℩ class. Usage of this theorem is discouraged because it depends on ax-13 2390. Use the weaker nfiotaw 6320 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 1805	. . 3 ⊢ Ⅎ𝑦⊤
2		nfiota.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3	2	a1i 11	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
4	1, 3	nfiotad 6321	. 2 ⊢ (⊤ → Ⅎ𝑥(℩𝑦𝜑))
5	4	mptru 1544	1 ⊢ Ⅎ𝑥(℩𝑦𝜑)

Syntax hints:  ⊤wtru 1538  Ⅎwnf 1784  Ⅎwnfc 2963  ℩cio 6314

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-10 2145  ax-11 2161  ax-12 2177  ax-13 2390  ax-ext 2795

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-tru 1540  df-ex 1781  df-nf 1785  df-sb 2070  df-clab 2802  df-cleq 2816  df-clel 2895  df-nfc 2965  df-ral 3145  df-rex 3146  df-v 3498  df-in 3945  df-ss 3954  df-sn 4570  df-uni 4841  df-iota 6316

This theorem is referenced by:  nfsum  15050