Theorem qimeqex-P5-L2 611

Description: Lemma for qimeqex-P5 612.

Assertion

Ref	Expression
qimeqex-P5-L2	⊢ (∃𝑥(𝜑 → 𝜓) → (∀𝑥𝜑 → ∃𝑥𝜓))

Proof of Theorem qimeqex-P5-L2

Step	Hyp	Ref	Expression
1		ndime-P3.6.CL 244	. . . 4 ⊢ ((𝜑 ∧ (𝜑 → 𝜓)) → 𝜓)
2	1	rcp-NDIMI2 224	. . 3 ⊢ (𝜑 → ((𝜑 → 𝜓) → 𝜓))
3	2	dalloverimex-P5.RC.GEN 607	. 2 ⊢ (∀𝑥𝜑 → (∃𝑥(𝜑 → 𝜓) → ∃𝑥𝜓))
4	3	imcomm-P3.27.RC 266	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:  qimeqex-P5  612  nfrim-P6  689