Theorem nfiotaw 5194

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 1476	. . 3 ⊢ Ⅎ𝑦⊤
2		nfiotaw.1	. . . 4 ⊢ Ⅎ𝑥𝜑
3	2	a1i 9	. . 3 ⊢ (⊤ → Ⅎ𝑥𝜑)
4	1, 3	nfiotadw 5193	. 2 ⊢ (⊤ → Ⅎ𝑥(℩𝑦𝜑))
5	4	mptru 1372	1 ⊢ Ⅎ𝑥(℩𝑦𝜑)

Syntax hints:  ⊤wtru 1364  Ⅎwnf 1470  Ⅎwnfc 2316  ℩cio 5188

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169

This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-rex 2471  df-sn 3610  df-uni 3822  df-iota 5190

This theorem is referenced by:  csbiotag  5221  nffv  5537  nfsum1  11378  nfsum  11379  nfcprod1  11576  nfcprod  11577