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Theorem equsex 2143
 Description: An equivalence related to implicit substitution. See equsexv 2085 for a version with a dv condition which does not require ax-13 2104. See equsexALT 2144 for an alternate proof. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 3-Oct-2016.) (Proof shortened by Wolf Lammen, 6-Feb-2018.)
Hypotheses
Ref Expression
equsex.nf
equsex.1
Assertion
Ref Expression
equsex

Proof of Theorem equsex
StepHypRef Expression
1 equsex.nf . . 3
2 equsex.1 . . . 4
32biimpa 492 . . 3
41, 3exlimi 2015 . 2
51, 2equsal 2141 . . 3
6 equs4 2140 . . 3
75, 6sylbir 218 . 2
84, 7impbii 192 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wa 376  wal 1450  wex 1671  wnf 1675 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-12 1950  ax-13 2104 This theorem depends on definitions:  df-bi 190  df-an 378  df-ex 1672  df-nf 1676 This theorem is referenced by:  equsexh  2145  sb5rf  2271
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