Theorem nfiota 6505

Description: Bound-variable hypothesis builder for the ℩ class. Usage of this theorem is discouraged because it depends on ax-13 2407. Use the weaker nfiotaw 6503 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 1837	. . 3 ⊢ Ⅎ𝑦⊤
2		nfiota.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3	2	a1i 11	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
4	1, 3	nfiotad 6504	. 2 ⊢ (⊤ → Ⅎ𝑥(℩𝑦𝜑))
5	4	mptru 1577	1 ⊢ Ⅎ𝑥(℩𝑦𝜑)

This proof depends on syntax axioms:  ⊤wtru 1571  Ⅎwnf 1816  Ⅎwnfc 2913  ℩cio 6497

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-10 2179  ax-11 2195  ax-12 2216  ax-13 2407  ax-ext 2738

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-nf 1817  df-sb 2100  df-clab 2745  df-cleq 2758  df-clel 2841  df-nfc 2915  df-ral 3083  df-rex 3093  df-v 3460  df-ss 3925  df-sn 4595  df-uni 4878  df-iota 6499

This theorem is used by: (None)