Theorem dalloverimex-P5.RC 606

Description: Inference Form of dalloverimex-P5 605.

Hypothesis

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

Assertion

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

Proof of Theorem dalloverimex-P5.RC

Step	Hyp	Ref	Expression
1		dalloverimex-P5.RC.1	. . . 4 ⊢ ∀𝑥(𝜑 → (𝜓 → 𝜒))
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → ∀𝑥(𝜑 → (𝜓 → 𝜒)))
3	2	dalloverimex-P5 605	. 2 ⊢ (⊤ → (∀𝑥𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒)))
4	3	ndtruee-P3.18 183	1 ⊢ (∀𝑥𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒))

Syntax hints:  ∀wff-forall 8   → wff-imp 10  ⊤wff-true 153  ∃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:  dalloverimex-P5.RC.GEN  607