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Theorem equsexh 1963
Description: A useful equivalence related to substitution. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
equsexh.1 (ψxψ)
equsexh.2 (x = y → (φψ))
Assertion
Ref Expression
equsexh (x(x = y φ) ↔ ψ)

Proof of Theorem equsexh
StepHypRef Expression
1 equsexh.1 . . 3 (ψxψ)
21nfi 1551 . 2 xψ
3 equsexh.2 . 2 (x = y → (φψ))
42, 3equsex 1962 1 (x(x = y φ) ↔ ψ)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   wa 358  wal 1540  wex 1541
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545
This theorem is referenced by:  cleljust  2014
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