Theorem 19.40 773

Description: Theorem 19.40 of [Margaris] p. 90.

Assertion

Ref	Expression
19.40	⊢ (∃x(φ ∧ ψ) → (∃xφ ∧ ∃xψ))

Proof of Theorem 19.40

Step	Hyp	Ref	Expression
1		pm3.26 256	. . 3 ⊢ ((φ ∧ ψ) → φ)
2	1	19.22i 723	. 2 ⊢ (∃x(φ ∧ ψ) → ∃xφ)
3		pm3.27 260	. . 3 ⊢ ((φ ∧ ψ) → ψ)
4	3	19.22i 723	. 2 ⊢ (∃x(φ ∧ ψ) → ∃xψ)
5	2, 4	jca 236	1 ⊢ (∃x(φ ∧ ψ) → (∃xφ ∧ ∃xψ))

Syntax hints:   → wi 2   ∧ wa 196  ∃wex 678

This theorem is referenced by:  euex 1021  elisset 1354  uniin 1935  dmin 2537  imadif 2714  fv3 2839

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-gen 677

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679

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