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Theorem r19.28av 2443
Description: Restricted version of one direction of Theorem 19.28 of [Margaris] p. 90. (The other direction doesn't hold when A is empty.) (Contributed by NM, 2-Apr-2004.)
Assertion
Ref Expression
r19.28av ((φ x A ψ) → x A (φ ψ))
Distinct variable group:   φ,x
Allowed substitution hints:   ψ(x)   A(x)

Proof of Theorem r19.28av
StepHypRef Expression
1 r19.27av 2442 . 2 ((x A ψ φ) → x A (ψ φ))
2 ancom 253 . 2 ((φ x A ψ) ↔ (x A ψ φ))
3 ancom 253 . . 3 ((φ ψ) ↔ (ψ φ))
43ralbii 2324 . 2 (x A (φ ψ) ↔ x A (ψ φ))
51, 2, 43imtr4i 190 1 ((φ x A ψ) → x A (φ ψ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wral 2300
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-5 1333  ax-gen 1335  ax-4 1397  ax-17 1416
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-ral 2305
This theorem is referenced by:  rr19.28v  2677  fununi  4908
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