Theorem alloverimex-P5.CL 604

Description: Closed Form of alloverimex-P5 601.

Assertion

Ref	Expression
alloverimex-P5.CL	⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))

Proof of Theorem alloverimex-P5.CL

Step	Hyp	Ref	Expression
1		rcp-NDASM1of1 192	. 2 ⊢ (∀𝑥(𝜑 → 𝜓) → ∀𝑥(𝜑 → 𝜓))
2	1	alloverimex-P5 601	1 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓))

Syntax hints:  ∀wff-forall 8   → wff-imp 10  ∃wff-exists 595

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14  ax-GEN 15  ax-L4 16

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-or-D2.3 145  df-true-D2.4 155  df-rcp-AND3 161  df-exists-D5.1 596

This theorem is referenced by:  qimeqallb-P6-L1  700  exi-P6  718  exipsub-P6  720  gennfrcl-L6  812