Users' Mathboxes Mathbox for Jonathan Ben-Naim < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj564 Structured version   Visualization version   GIF version

Theorem bnj564 29874
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypothesis
Ref Expression
bnj564.17 (𝜏 ↔ (𝑓 Fn 𝑚𝜑′𝜓′))
Assertion
Ref Expression
bnj564 (𝜏 → dom 𝑓 = 𝑚)

Proof of Theorem bnj564
StepHypRef Expression
1 bnj564.17 . . 3 (𝜏 ↔ (𝑓 Fn 𝑚𝜑′𝜓′))
21simp1bi 1068 . 2 (𝜏𝑓 Fn 𝑚)
3 fndm 5890 . 2 (𝑓 Fn 𝑚 → dom 𝑓 = 𝑚)
42, 3syl 17 1 (𝜏 → dom 𝑓 = 𝑚)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194  w3a 1030   = wceq 1474  dom cdm 5028   Fn wfn 5785
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 195  df-an 384  df-3an 1032  df-fn 5793
This theorem is referenced by:  bnj570  30035  bnj916  30063
  Copyright terms: Public domain W3C validator