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Theorem rsp2e 2366
Description: Restricted specialization. (Contributed by FL, 4-Jun-2012.)
Assertion
Ref Expression
rsp2e ((x A y B φ) → x A y B φ)

Proof of Theorem rsp2e
StepHypRef Expression
1 simp1 903 . . 3 ((x A y B φ) → x A)
2 rspe 2364 . . . 4 ((y B φ) → y B φ)
323adant1 921 . . 3 ((x A y B φ) → y B φ)
4 19.8a 1479 . . 3 ((x A y B φ) → x(x A y B φ))
51, 3, 4syl2anc 391 . 2 ((x A y B φ) → x(x A y B φ))
6 df-rex 2306 . 2 (x A y B φx(x A y B φ))
75, 6sylibr 137 1 ((x A y B φ) → x A y B φ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   w3a 884  wex 1378   wcel 1390  wrex 2301
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397
This theorem depends on definitions:  df-bi 110  df-3an 886  df-rex 2306
This theorem is referenced by: (None)
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