Theorem mobidv 2239

Description: Formula-building rule for "at most one" quantifier (deduction rule). (Contributed by Mario Carneiro, 7-Oct-2016.)

Hypothesis

Ref	Expression
mobidv.1	⊢ (φ → (ψ ↔ χ))

Assertion

Ref	Expression
mobidv	⊢ (φ → (∃*xψ ↔ ∃*xχ))

Distinct variable group:   φ,x

Allowed substitution hints:   ψ(x)   χ(x)

Proof of Theorem mobidv

Step	Hyp	Ref	Expression
1		nfv 1619	. 2 ⊢ Ⅎxφ
2		mobidv.1	. 2 ⊢ (φ → (ψ ↔ χ))
3	1, 2	mobid 2238	1 ⊢ (φ → (∃*xψ ↔ ∃*xχ))

Syntax hints:   → wi 4   ↔ wb 176  ∃*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-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545  df-eu 2208  df-mo 2209

This theorem is referenced by:  mobii  2240  mosubopt  4613  dffun6f  5124  funmo  5126