New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  iotabidv GIF version

Theorem iotabidv 4360
 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 1631 . 2 (φx(ψχ))
3 iotabi 4348 . 2 (x(ψχ) → (℩xψ) = (℩xχ))
42, 3syl 15 1 (φ → (℩xψ) = (℩xχ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∀wal 1540   = wceq 1642  ℩cio 4337 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620  df-uni 3892  df-iota 4339 This theorem is referenced by:  csbiotag  4371  ncfineq  4473  tfineq  4488  fveq1  5327  fveq2  5328  csbfv12g  5336  fvres  5342  tceq  6158
 Copyright terms: Public domain W3C validator