Theorem mobidv 2122

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

Hypothesis

Ref	Expression
mobidv.1	|- ( ph -> ( ps <-> ch ) )

Assertion

Ref	Expression
mobidv	|- ( ph -> ( E* x ps <-> E* x ch ) )

Distinct variable group:   ph, x

Allowed substitution hints:   ps( x)   ch( x)

Proof of Theorem mobidv

Step	Hyp	Ref	Expression
1		nfv 1581	. 2 |- F/ x ph
2		mobidv.1	. 2 |- ( ph -> ( ps <-> ch ) )
3	1, 2	mobid 2121	1 |- ( ph -> ( E* x ps <-> E* x ch ) )

This proof depends on syntax axioms:   -> wi 4   <-> wb 105   E*wmo 2087

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-4 1563  ax-17 1579  ax-ial 1587

This proof depends on definitions:  df-bi 117  df-nf 1514  df-eu 2089  df-mo 2090

This theorem is used by:  mobii  2123  mosubopt  4840  dffun6f  5390  funmo  5392  1stconst  6457  2ndconst  6458  exmidmotap  7627  imasaddfnlemg  13635  dvfgg  15789