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Theorem spv 1998
 Description: Specialization, using implicit substitution. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
spv.1 (x = y → (φψ))
Assertion
Ref Expression
spv (xφψ)
Distinct variable group:   ψ,x
Allowed substitution hints:   φ(x,y)   ψ(y)

Proof of Theorem spv
StepHypRef Expression
1 spv.1 . . 3 (x = y → (φψ))
21biimpd 198 . 2 (x = y → (φψ))
32spimv 1990 1 (xφψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∀wal 1540 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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:  chvarv  2013  ax10-16  2190  ru  3045  sfintfin  4532  spfinsfincl  4539
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