Theorem simpld 37

Description: Extract an assumption from the context. (Contributed by Mario Carneiro, 8-Oct-2014.)

Hypothesis

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

Assertion

Ref	Expression
simpld	|- R |= S

Proof of Theorem simpld

Step	Hyp	Ref	Expression
1		simpld.1	. 2 |- R |= (S, T)
2	1	ax-cb2 30	. . . 4 |- (S, T):*
3	2	wctl 33	. . 3 |- S:*
4	2	wctr 34	. . 3 |- T:*
5	3, 4	simpl 22	. 2 |- (S, T) |= S
6	1, 5	syl 16	1 |- R |= S

Syntax hints:  kct 10   |= wffMMJ2 11

This theorem was proved from axioms:  ax-syl 15  ax-simpl 20  ax-cb2 30  ax-wctl 31  ax-wctr 32

This theorem is referenced by:  ex  158  exmid  199  ax2  204