Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfiotaw GIF version

Theorem nfiotaw 5092
 Description: Bound-variable hypothesis builder for the ℩ class. (Contributed by NM, 23-Aug-2011.)
Hypothesis
Ref Expression
nfiotaw.1 𝑥𝜑
Assertion
Ref Expression
nfiotaw 𝑥(℩𝑦𝜑)
Distinct variable group:   𝑥,𝑦
Allowed substitution hints:   𝜑(𝑥,𝑦)

Proof of Theorem nfiotaw
StepHypRef Expression
1 nftru 1442 . . 3 𝑦
2 nfiotaw.1 . . . 4 𝑥𝜑
32a1i 9 . . 3 (⊤ → Ⅎ𝑥𝜑)
41, 3nfiotadw 5091 . 2 (⊤ → 𝑥(℩𝑦𝜑))
54mptru 1340 1 𝑥(℩𝑦𝜑)
 Colors of variables: wff set class Syntax hints:  ⊤wtru 1332  Ⅎwnf 1436  Ⅎwnfc 2268  ℩cio 5086 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rex 2422  df-sn 3533  df-uni 3737  df-iota 5088 This theorem is referenced by:  csbiotag  5116  nffv  5431  nfsum1  11132  nfsum  11133  nfcprod1  11330  nfcprod  11331
 Copyright terms: Public domain W3C validator