Theorem moimi 2251

Description: "At most one" is preserved through implication (notice wff reversal). (Contributed by NM, 15-Feb-2006.)

Hypothesis

Ref	Expression
immoi.1	⊢ (φ → ψ)

Assertion

Ref	Expression
moimi	⊢ (∃*xψ → ∃*xφ)

Proof of Theorem moimi

Step	Hyp	Ref	Expression
1		moim 2250	. 2 ⊢ (∀x(φ → ψ) → (∃*xψ → ∃*xφ))
2		immoi.1	. 2 ⊢ (φ → ψ)
3	1, 2	mpg 1548	1 ⊢ (∃*xψ → ∃*xφ)

Syntax hints:   → wi 4  ∃*wmo 2205

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209

This theorem is referenced by:  moan  2255  moor  2257  mooran1  2258  mooran2  2259  2moex  2275  2euex  2276  2exeu  2281  2eu1  2284  nfunsn  5354  caovmo  5646