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Theorem r19.40 2433
Description: Restricted quantifier version of Theorem 19.40 of [Margaris] p. 90. (Contributed by NM, 2-Apr-2004.)
Assertion
Ref Expression
r19.40 (x A (φ ψ) → (x A φ x A ψ))

Proof of Theorem r19.40
StepHypRef Expression
1 simpl 102 . . 3 ((φ ψ) → φ)
21reximi 2385 . 2 (x A (φ ψ) → x A φ)
3 simpr 103 . . 3 ((φ ψ) → ψ)
43reximi 2385 . 2 (x A (φ ψ) → x A ψ)
52, 4jca 290 1 (x A (φ ψ) → (x A φ x A ψ))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wrex 2276
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 1309  ax-gen 1311  ax-ie1 1355  ax-ie2 1356  ax-4 1373  ax-ial 1400
This theorem depends on definitions:  df-bi 110  df-ral 2280  df-rex 2281
This theorem is referenced by: (None)
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