Theorem nfiotaw 5164

Description: Bound-variable hypothesis builder for the ℩ class. (Contributed by NM, 23-Aug-2011.)

Hypothesis

Ref	Expression
nfiotaw.1	⊢ Ⅎ𝑥𝜑

Assertion

Ref	Expression
nfiotaw	⊢ Ⅎ𝑥(℩𝑦𝜑)

Distinct variable group:   𝑥,𝑦

Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem nfiotaw

Step	Hyp	Ref	Expression
1		nftru 1459	. . 3 ⊢ Ⅎ𝑦⊤
2		nfiotaw.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3	2	a1i 9	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
4	1, 3	nfiotadw 5163	. 2 ⊢ (⊤ → Ⅎ𝑥(℩𝑦𝜑))
5	4	mptru 1357	1 ⊢ Ⅎ𝑥(℩𝑦𝜑)

Syntax hints:  ⊤wtru 1349  Ⅎwnf 1453  Ⅎwnfc 2299  ℩cio 5158

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-rex 2454  df-sn 3589  df-uni 3797  df-iota 5160

This theorem is referenced by:  csbiotag  5191  nffv  5506  nfsum1  11319  nfsum  11320  nfcprod1  11517  nfcprod  11518