Theorem eqeqan12dALT 2639

Description: Alternate proof of eqeqan12d 2638. This proof has one more step but one fewer essential step. (Contributed by NM, 9-Aug-1994.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
eqeqan12d.1	|- ( ph -> A = B )
eqeqan12d.2	|- ( ps -> C = D )

Assertion

Ref	Expression
eqeqan12dALT	|- ( ( ph /\ ps ) -> ( A = C <-> B = D ) )

Proof of Theorem eqeqan12dALT

Step	Hyp	Ref	Expression
1		eqeqan12d.1	. 2 |- ( ph -> A = B )
2		eqeqan12d.2	. 2 |- ( ps -> C = D )
3		eqeq12 2635	. 2 |- ( ( A = B /\ C = D ) -> ( A = C <-> B = D ) )
4	1, 2, 3	syl2an 494	1 |- ( ( ph /\ ps ) -> ( A = C <-> B = D ) )

Syntax hints:   -> wi 4   <-> wb 196   /\ wa 384   = wceq 1483

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-9 1999  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-cleq 2615

This theorem is referenced by: (None)