Theorem moan 2512

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 476	. 2 ⊢ ((𝜓 ∧ 𝜑) → 𝜑)
2	1	moimi 2508	1 ⊢ (∃*𝑥𝜑 → ∃*𝑥(𝜓 ∧ 𝜑))

Syntax hints:   → wi 4   ∧ wa 383  ∃*wmo 2459

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-12 2034

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-eu 2462  df-mo 2463

This theorem is referenced by:  moani  2513  mooran1  2515  moanim  2517  mormo  3135  rmoan  3373