Theorem moan 2552

Description: "At most one" is still the case when a conjunct is added. (Contributed by NM, 22-Apr-1995.)

Assertion

Ref	Expression
moan	⊢ (∃*𝑥𝜑 → ∃*𝑥(𝜓 ∧ 𝜑))

Proof of Theorem moan

Step	Hyp	Ref	Expression
1		simpr 484	. 2 ⊢ ((𝜓 ∧ 𝜑) → 𝜑)
2	1	moimi 2545	1 ⊢ (∃*𝑥𝜑 → ∃*𝑥(𝜓 ∧ 𝜑))

Syntax hints:   → wi 4   ∧ wa 395  ∃*wmo 2538

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

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-mo 2540

This theorem is referenced by:  moani  2553  mooran1  2555  moanimlem  2618  mormo  3385  rmoan  3745