Theorem dalloverimex-P5.RC.GEN 607

Description: Inference Form of dalloverimex-P5 605 with Generalization.

Hypothesis

Ref	Expression
dalloverimex-P5.RC.GEN.1	⊢ (𝜑 → (𝜓 → 𝜒))

Assertion

Ref	Expression
dalloverimex-P5.RC.GEN	⊢ (∀𝑥𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))

Proof of Theorem dalloverimex-P5.RC.GEN

Step	Hyp	Ref	Expression
1		dalloverimex-P5.RC.GEN.1	. . 3 ⊢ (𝜑 → (𝜓 → 𝜒))
2	1	ax-GEN 15	. 2 ⊢ ∀𝑥(𝜑 → (𝜓 → 𝜒))
3	2	dalloverimex-P5.RC 606	1 ⊢ (∀𝑥𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))

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:  qimeqex-P5-L2  611  qimeqallbv-P5-L1  619  lemma-L5.02a  653  lemma-L6.04a  749