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Theorem iotabidv 4815
Description: Formula-building deduction rule for iota. (Contributed by NM, 20-Aug-2011.)
Hypothesis
Ref Expression
iotabidv.1 (φ → (ψχ))
Assertion
Ref Expression
iotabidv (φ → (℩xψ) = (℩xχ))
Distinct variable group:   φ,x
Allowed substitution hints:   ψ(x)   χ(x)

Proof of Theorem iotabidv
StepHypRef Expression
1 iotabidv.1 . . 3 (φ → (ψχ))
21alrimiv 1736 . 2 (φx(ψχ))
3 iotabi 4803 . 2 (x(ψχ) → (℩xψ) = (℩xχ))
42, 3syl 14 1 (φ → (℩xψ) = (℩xχ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wal 1226   = wceq 1228  cio 4792
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-rex 2290  df-uni 3555  df-iota 4794
This theorem is referenced by:  csbiotag  4822  dffv3g  5099  fveq1  5102  fveq2  5103  fvres  5123  csbfv12g  5134  fvco2  5167  riotaeqdv  5394  riotabidv  5395  riotabidva  5408  ovtposg  5796
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