Theorem moimiOLD 2627

Description: Obsolete version of moimi 2626 as of 9-May-2023. The at-most-one quantifier reverses implication. (Contributed by NM, 15-Feb-2006.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
moimiOLD.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
moimiOLD	⊢ (∃*𝑥𝜓 → ∃*𝑥𝜑)

Proof of Theorem moimiOLD

Step	Hyp	Ref	Expression
1		moim 2625	. 2 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃*𝑥𝜓 → ∃*𝑥𝜑))
2		moimiOLD.1	. 2 ⊢ (𝜑 → 𝜓)
3	1, 2	mpg 1797	1 ⊢ (∃*𝑥𝜓 → ∃*𝑥𝜑)

Syntax hints:   → wi 4  ∃*wmo 2619

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910

This theorem depends on definitions:  df-bi 209  df-ex 1780  df-mo 2621

This theorem is referenced by: (None)