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Theorem spcimgf 2932
 Description: Rule of specialization, using implicit substitution. Compare Theorem 7.3 of [Quine] p. 44. (Contributed by Mario Carneiro, 4-Jan-2017.)
Hypotheses
Ref Expression
spcimgf.1 xA
spcimgf.2 xψ
spcimgf.3 (x = A → (φψ))
Assertion
Ref Expression
spcimgf (A V → (xφψ))

Proof of Theorem spcimgf
StepHypRef Expression
1 spcimgf.2 . . 3 xψ
2 spcimgf.1 . . 3 xA
31, 2spcimgft 2930 . 2 (x(x = A → (φψ)) → (A V → (xφψ)))
4 spcimgf.3 . 2 (x = A → (φψ))
53, 4mpg 1548 1 (A V → (xφψ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1540  Ⅎwnf 1544   = wceq 1642   ∈ wcel 1710  Ⅎwnfc 2476 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  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861 This theorem is referenced by:  spcimegf  2933
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