Theorem trul 39

Description: Deduction form of tru 44. (Contributed by Mario Carneiro, 7-Oct-2014.)

Hypothesis

Ref	Expression
trul.1	|- (T., R) |= S

Assertion

Ref	Expression
trul	|- R |= S

Proof of Theorem trul

Step	Hyp	Ref	Expression
1		trul.1	. . . . 5 |- (T., R) |= S
2	1	ax-cb1 29	. . . 4 |- (T., R):*
3	2	wctr 34	. . 3 |- R:*
4	3	trud 27	. 2 |- R |= T.
5	3	id 25	. 2 |- R |= R
6	4, 5, 1	syl2anc 19	1 |- R |= S

Syntax hints:  T.kt 8  kct 10   |= wffMMJ2 11

This theorem was proved from axioms:  ax-syl 15  ax-jca 17  ax-id 24  ax-trud 26  ax-cb1 29  ax-wctr 32

This theorem is referenced by:  alnex  186  exnal1  187