Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  spim Structured version   Unicode version

Theorem spim 2062
 Description: Specialization, using implicit substitution. Compare Lemma 14 of [Tarski] p. 70. The spim 2062 series of theorems requires that only one direction of the substitution hypothesis hold. (Contributed by NM, 10-Jan-1993.) (Revised by Mario Carneiro, 3-Oct-2016.) (Proof shortened by Wolf Lammen, 18-Feb-2018.)
Hypotheses
Ref Expression
spim.1
spim.2
Assertion
Ref Expression
spim

Proof of Theorem spim
StepHypRef Expression
1 spim.1 . 2
2 ax6e 2058 . . 3
3 spim.2 . . 3
42, 3eximii 1705 . 2
51, 419.36i 2022 1
 Colors of variables: wff setvar class Syntax hints:   wi 4  wal 1435  wnf 1663 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-12 1907  ax-13 2055 This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1660  df-nf 1664 This theorem is referenced by:  spimv  2065  chvar  2069  cbv3  2071
 Copyright terms: Public domain W3C validator