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Theorem ralimdaa 2380
Description: Deduction quantifying both antecedent and consequent, based on Theorem 19.20 of [Margaris] p. 90. (Contributed by NM, 22-Sep-2003.)
Hypotheses
Ref Expression
ralimdaa.1 xφ
ralimdaa.2 ((φ x A) → (ψχ))
Assertion
Ref Expression
ralimdaa (φ → (x A ψx A χ))

Proof of Theorem ralimdaa
StepHypRef Expression
1 ralimdaa.1 . . 3 xφ
2 ralimdaa.2 . . . . 5 ((φ x A) → (ψχ))
32ex 108 . . . 4 (φ → (x A → (ψχ)))
43a2d 23 . . 3 (φ → ((x Aψ) → (x Aχ)))
51, 4alimd 1411 . 2 (φ → (x(x Aψ) → x(x Aχ)))
6 df-ral 2305 . 2 (x A ψx(x Aψ))
7 df-ral 2305 . 2 (x A χx(x Aχ))
85, 6, 73imtr4g 194 1 (φ → (x A ψx A χ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wal 1240  wnf 1346   wcel 1390  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
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-ral 2305
This theorem is referenced by:  ralimdva  2381
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