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Theorem spcgv 2939
 Description: Rule of specialization, using implicit substitution. Compare Theorem 7.3 of [Quine] p. 44. (Contributed by NM, 22-Jun-1994.)
Hypothesis
Ref Expression
spcgv.1 (x = A → (φψ))
Assertion
Ref Expression
spcgv (A V → (xφψ))
Distinct variable groups:   ψ,x   x,A
Allowed substitution hints:   φ(x)   V(x)

Proof of Theorem spcgv
StepHypRef Expression
1 nfcv 2489 . 2 xA
2 nfv 1619 . 2 xψ
3 spcgv.1 . 2 (x = A → (φψ))
41, 2, 3spcgf 2934 1 (A V → (xφψ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∀wal 1540   = wceq 1642   ∈ wcel 1710 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  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:  spcv  2945  mob2  3016  intss1  3941  dfiin2g  4000  sfintfin  4532  funmo  5125  frd  5922
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