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Theorem equs45f 2088
 Description: Two ways of expressing substitution when is not free in . (Contributed by NM, 25-Apr-2008.) (Revised by Mario Carneiro, 4-Oct-2016.)
Hypothesis
Ref Expression
equs45f.1
Assertion
Ref Expression
equs45f

Proof of Theorem equs45f
StepHypRef Expression
1 equs45f.1 . . . . . 6
21nfri 1778 . . . . 5
32anim2i 553 . . . 4
43eximi 1585 . . 3
5 equs5a 1909 . . 3
64, 5syl 16 . 2
7 equs4 1997 . 2
86, 7impbii 181 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549  wex 1550  wnf 1553 This theorem is referenced by:  sb5f  2123 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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