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Theorem elv 2662
Description: Technical lemma used to shorten proofs. If a proposition is implied by 𝑥 ∈ V (which is true, see vex 2661), then it is true. (Contributed by Peter Mazsa, 13-Oct-2018.)
Hypothesis
Ref Expression
elv.1 (𝑥 ∈ V → 𝜑)
Assertion
Ref Expression
elv 𝜑

Proof of Theorem elv
StepHypRef Expression
1 vex 2661 . 2 𝑥 ∈ V
2 elv.1 . 2 (𝑥 ∈ V → 𝜑)
31, 2ax-mp 5 1 𝜑
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1463  Vcvv 2658
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-5 1406  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-v 2660
This theorem is referenced by:  xpiindim  4644  disjxp1  6099  ixpiinm  6584  ixpsnf1o  6596  iunfidisj  6800  ssfii  6828  fifo  6834  omp1eomlem  6945  exmidomniim  6979  bcval5  10449  rexfiuz  10701  fsum2dlemstep  11143  fsumcnv  11146  fisumcom2  11147  fsumconst  11163  modfsummodlemstep  11166  fsumabs  11174  ennnfonelemim  11832  topnfn  12020  iuncld  12179  txbas  12322  txdis  12341  xmetunirn  12422  xmettxlem  12573  xmettx  12574
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