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Theorem spcgf 2934
 Description: Rule of specialization, using implicit substitution. Compare Theorem 7.3 of [Quine] p. 44. (Contributed by NM, 2-Feb-1997.) (Revised by Andrew Salmon, 12-Aug-2011.)
Hypotheses
Ref Expression
spcgf.1 xA
spcgf.2 xψ
spcgf.3 (x = A → (φψ))
Assertion
Ref Expression
spcgf (A V → (xφψ))

Proof of Theorem spcgf
StepHypRef Expression
1 spcgf.2 . . 3 xψ
2 spcgf.1 . . 3 xA
31, 2spcgft 2931 . 2 (x(x = A → (φψ)) → (A V → (xφψ)))
4 spcgf.3 . 2 (x = A → (φψ))
53, 4mpg 1548 1 (A V → (xφψ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∀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:  spcegf  2935  spcgv  2939  rspc  2949  elabgt  2982
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