Theorem moani 2045

Description: "At most one" is still true when a conjunct is added. (Contributed by NM, 9-Mar-1995.)

Hypothesis

Ref	Expression
moani.1	⊢ ∃*𝑥𝜑

Assertion

Ref	Expression
moani	⊢ ∃*𝑥(𝜓 ∧ 𝜑)

Proof of Theorem moani

Step	Hyp	Ref	Expression
1		moani.1	. 2 ⊢ ∃*𝑥𝜑
2		moan 2044	. 2 ⊢ (∃*𝑥𝜑 → ∃*𝑥(𝜓 ∧ 𝜑))
3	1, 2	ax-mp 7	1 ⊢ ∃*𝑥(𝜓 ∧ 𝜑)

Syntax hints:   ∧ wa 103  ∃*wmo 1976

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498

This theorem depends on definitions:  df-bi 116  df-nf 1420  df-sb 1719  df-eu 1978  df-mo 1979

This theorem is referenced by:  euxfr2dc  2838  fvopab6  5471  1stconst  6072  2ndconst  6073  axaddf  7603  axmulf  7604