Theorem exlimiieq2 32822

Description: Inferring a theorem when it is implied by an equality which may be true. (Contributed by BJ, 15-Sep-2018.) (Revised by BJ, 30-Sep-2018.)

Hypotheses

Ref	Expression
exlimiieq2.1	|- F/ y ph
exlimiieq2.2	|- ( x = y -> ph )

Assertion

Ref	Expression
exlimiieq2	|- ph

Proof of Theorem exlimiieq2

Step	Hyp	Ref	Expression
1		exlimiieq2.1	. 2 |- F/ y ph
2		exlimiieq2.2	. 2 |- ( x = y -> ph )
3		ax6er 32820	. 2 |- E. y x = y
4	1, 2, 3	exlimii 32818	1 |- ph

Syntax hints:   -> wi 4   F/wnf 1708

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710

This theorem is referenced by: (None)